Vova again tries to play some computer card game.

The rules of deck creation in this game are simple. Vova is given an existing deck of n cards and a magic number k. The order of the cards in the deck is fixed. Each card has a number written on it; number ai is written on the i-th card in the deck.

After receiving the deck and the magic number, Vova removes x (possibly x = 0) cards from the top of the deck, y (possibly y = 0) cards from the bottom of the deck, and the rest of the deck is his new deck (Vova has to leave at least one card in the deck after removing cards). So Vova's new deck actually contains cards x + 1, x + 2, ... n - y - 1, n - y from the original deck.

Vova's new deck is considered valid iff the product of all numbers written on the cards in his new deck is divisible by k. So Vova received a deck (possibly not a valid one) and a number k, and now he wonders, how many ways are there to choose x and y so the deck he will get after removing x cards from the top and y cards from the bottom is valid?

Input

The first line contains two integers n and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ 109).

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the numbers written on the cards.

Output

Print the number of ways to choose x and y so the resulting deck is valid.

Examples

Input

3 4
6 2 8


Output

4


Input

3 6
9 1 14


Output

1

Note

In the first example the possible values of x and y are:

  1. x = 0, y = 0; 
  2. x = 1, y = 0; 
  3. x = 2, y = 0; 
  4. x = 0, y = 1. 
                                    import java.util.*; 
                                    import java.math.*;
                                    import java.io.*;
                                    import java.text.DecimalFormat;
                                    import java.math.BigInteger;
                                    public class Main{
                                        //static int d=20;
                                        static long mod=1000000007 ;
                                        
                                        static ArrayList<ArrayList<Edge>> arr;
                                       // static long[] dp1,dp2;
                                        static int[] a;
                                        static int[] vis,num;
                                        static long max;
                                        static HashSet<String> hs;
                                        //static int flag,ans;
                                        static long max1,max2,ans1;
                                        
                                        static int flag=0;
                                        static int[] tin,tout,parent,level;
                                        static HashMap<Long,Integer> hm;
                                        static long[] dp1,dp2,dp3,dp4;
                                        static int ct=0;
                                           
                                        public static void main(String[] args)  throws IOException {
                                            ///long start=System.currentTimeMillis();
                                            boolean online =false  ;
                                            String fileName = "C-large-practice";
                                            PrintWriter out; 
                                            if (online) {
                                                s.init(new FileInputStream(new File("Downloads/"+fileName + ".in")));
                                                 out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                            }
                                             else {
                                                s.init(System.in);   
                                            
                                                out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
                                                //out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                            }//r,b,y,g
                                            int n;
                                            n=s.ni();
                                            long k=s.ni();
                                            long ans=0;
                                            long[] a=new long[n];
                                            for(int i=0;i<n;i++)
                                                a[i]=s.nl();
                                            int flag=0;
                                            int last=-1;
                                            int j=0;
                                            long mod=1;
                                            for(int i=0;i<n;){
                                                
                                          
                                               for(;j<n;j++){
                                                    mod*=a[j]%k;
                                                    mod%=k;
                                                    if(mod==0)
                                                        break;

                                               }

                                               if(mod!=0)
                                                    break;
                                                int k2=j;
                                                mod=1;
                                                long mod2=1;
                                                long l=j;
                                                //System.out.println(i+" "+j);    
                                               for(;k2>=i;k2--){
                                                    mod*=a[k2]%k;
                                                    mod%=k;
                                                    if(mod==0)
                                                        break;
                                                    mod2*=(a[k2]%k);
                                                    mod2%=k;

                                               }
                                               
                                                ans+=(n-j)*1L*(k2-last);
                                                //out.println(k2+" "+j+" "+last+" "+ans);
                                                mod=1;

                                                last=k2;
                                                i=k2+1;
                                                j=j+1;
                                                if(j>=n)
                                                    break;
                                                mod=mod2;


                                            }
                                            out.println(ans);

                                            out.close();    
                                    
                                        }   
                                      
                                        
                                        public static int gcd(int a, int b){
                                                if (a == 0) return b;
                                                return gcd(b % a, a);
                                        }
                                            
                                        public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
                                            vis[c]=1;
                                            if(g!=-1){
                                                if(!arr.get(c).contains(g)){
                                                    flag=1;
                                                    return;
                                                }
                                            }
                                            for(int x:arr.get(c)){
                                                if(x!=p && x!=g && vis[x]==0 ){
                                                    cfs(arr,x,c,p,vis);
                                                }
                                            }
 
                                        }
                                                              //   public static void dfs(int u,int p){
         //                            //       if(p>=0)
         //                            //           tin[u]=tout[u]=tt++;
         //                            //       if(p>=0)
         //                            //           level[u]=level[p]+1;
         //                            //       parent[u]=p;
         //                            //       for(int x:arr.get(u)){
         //                            //           if(x!=p){
         //                            //               dfs(x,u);
         //                            //               tout[u]=Math.max(tout[u],tout[x]);
         //                            //           }
         //                            //       }
         //                            //       
         //
         //
                                     //   }
                                        public static int lca(int[][] p,int a,int b){
                                            if(level[a]<level[b]){
                                                int x=a;
                                                a=b;
                                                b=x;
                                            }
                                            int log=p[0].length;
                                            for(int i=log-1;i>=0;i--){
                                                if(1<<i<=level[a]-level[b]){
                                                    a=p[a][i];
                                                }
                                            }
                                            if(a==b)
                                                return a;
                                            for(int i=log-1;i>=0;i--){
                                                if(p[a][i]!=p[b][i]){
                                                    a=p[a][i];
                                                    b=p[b][i];
                                                }
                                            }
                                            return p[a][0];
         
                                        }
                                        public static int[][] par(int[] parent){
                                            int n=arr.size();
                                            int[][] p=new int[n][17];
                                            for(int i=0;i<n;i++)
                                                p[i][0]=parent[i];
                                            for(int k=1;k<17;k++){
                                                for(int i=0;i<n;i++){
                                                    if(p[i][k-1]>-1)
                                                        p[i][k]=p[p[i][k-1]][k-1];
                                                    else
                                                        p[i][k]=-1;
                                                }
                                            }
                                            return p;
                                        }
                                        static class Edge {
                                               int from;
                                                int to;
                                                int cost;
                                        
                                               public Edge(int from, int to, int weight) {
                                                   this.from = from;
                                                   this.to = to;
                                                   this.cost= weight;
                                               }
                                        }                               
                                        static class Node {
                                            int start;
                                            int end;
                        
                                            int cost;
                                            int updated;
                        
                                            Node[] nodes;
                        
                                            public Node(int start, int end) {
                                                this.start = start;
                                                this.end = end;
                        
                                                if (start < end) {
                                                    int[] pos = {start, (start + end) / 2, end};
                                                    nodes = new Node[2];
                                                    for (int i = 0; i < 2; i++) {
                                                        nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                                                    }
                                                }
                                            }
                        
                                            public void update(int queryStart, int queryEnd, int value) {
                                                if (queryEnd < start || end < queryStart) {
                                                    return;
                                                }
                        
                                                if (queryStart <= start && end <= queryEnd) {
                                                    cost += value;
                                                    updated += value;
                                                    return;
                                                }
                        
                                                propagate();
                                                for (Node node: nodes) {
                                                    node.update(queryStart, queryEnd, value);
                                                }
                                            }
                        
                                            public int query(int pos) {
                                                if (pos < start || end < pos) {
                                                    return 0;
                                                }
                        
                                                if (start == end) {
                                                    return cost;
                                                }
                        
                                                propagate();
                                                int ans = 0;
                                                for (Node node: nodes) {
                                                    ans = Math.max(ans, node.query(pos));
                                                }
                                                return ans;
                                            }
                        
                                            public void propagate() {
                                                if (updated != 0 && start < end) {
                                                    for (Node node: nodes) {
                                                        node.cost += updated;
                                                        node.updated += updated;
                                                    }
                                                    updated = 0;
                                                }
                                            }
                                        }
                                        public static double nthroot(int n, double A) {
                                            return nthroot(n, A, 0.0000001);
                                        }
                                        public static double nthroot(int n, double A, double p) {
                                            if(A < 0) {
                                                System.err.println("A < 0");// we handle only real positive numbers
                                                return -1;
                                            } else if(A == 0) {
                                                return 0;
                                            }
                                            double x_prev = A;
                                            double x = A / n;  // starting "guessed" value...
                                            while(Math.abs(x - x_prev) > p) {
                                                x_prev = x;
                                                x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
                                            }
                                            return x;
                                        }
                                        
                                        static class item implements Comparable<item> {
                                            int id,occ;
                                            public item(int x,int y){
                                                id=x;
                                                occ=y;
                                                
                                            }
                                            public int compareTo(item o){
                                                return  o.occ-occ;
                                            }
                                            
                                        }
                                       
                                        public static void dfs2(int c,int p,int[] a){
                                            //System.out.println(c+" "+p);
                                           
                                            
                                            
                 
                                        }
        //public static void dfs(int x,int[] vis,Stack<Integer> st){
                                        //    vis[x]=1;
                                        //    ArrayList<Integer> arr2=arr.get(x);
                                        //    Collections.sort(arr2);
                                        //    for(int i=arr2.size()-1;i>=0;i--){
                                        //        int z=arr2.get(i);
                                        //        if(vis[z]==0)
                                        //            dfs(z,vis,st);
                                        //    }
                                        //    st.push(x);
                 //
                                        //}
                                        public static long gcd(long a, long b){
                                                if (a == 0) return b;
                                                return gcd(b % a, a);
                                        }
                                            
                                        public static boolean check(long x){
                                            if(x%4==0 || x%7==0 || x%11==0)
                                                return true;
                                            if(x<4 || x<7 || x<11)
                                                return false;
                                            if(x%2==0){
                                                return check(x/2);
                                            }
                                            else
                                                return check(x/2) && check((x+1)/2);
                                        }
                                        public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
                                            long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
                                            if(val<0)
                                                return 1;
                                            else if(val>0)
                                                return -1;
                                            else
                                                return 0;
                                        }
                                        
                                        static class BIT{
                                        
                                            int N;
                                            long tree[];
                                            
                                            BIT(int N){
                                                this.N = N;
                                                tree = new long[N + 1];
                                            }
                                            
                                            void update(int idx,long val){
                                                while(idx <= N){
                                                    tree[idx]+=val;
                                                    idx += (idx & -idx);
                                                }
                                            }
                                            
                                            long query(int l,int r){
                                                if(l == 1)
                                                    return read(r);
                                                else
                                                    return read(r) - read(l-1);
                                            }
                                            
                                            long read(int idx){
                                                long sum = 0;
                                                while(idx > 0){
                                                    sum += tree[idx];
                                                    idx -= (idx & -idx);
                                                }
                                                return sum;
                                            }
                                        }
                                        public static boolean pal(String a){
                                            int i=0;
                                            int j=a.length()-1;
                                            while(i<j){
                                                if(a.charAt(i)!=a.charAt(j)){
                                                    return false;
                                                }
                                                i++;
                                                j--;
                                            }
                                            return true;
                                                
                                        }
                                        public static long find(long n,long k){
                                            if(n==2){
                                                if(k==1 || k==3)
                                                    return 1;
                                                else
                                                    return 2;
                                            }
                                            long t=pow2(2,n,mod)-1;
                                            long z=(t+1)/2;
                                            if(k==z)
                                                return n;
                                            if(k<z)
                                                return find(n-1,k);
                                            else
                                                return find(n-1,k-z);
                                        }
                                        public static long pow2(long a,long b,long mod){
                                                
                                                long ans=1;
                                               // long z=b;
                                                while(b>0){
                                                   
                                                    if(b%2==1)
                                                        ans=(a*ans)%mod;
                                                    a=(a*a)%mod;
                                                    b/=2;
                                                }
                                              
                                                return  ans;
                                        }
                                         public static long pow3(long a,long b){
                                                
                                                long ans=1;
                                               // long z=b;
                                                while(b>0){
                                                   
                                                    if(b%2==1)
                                                        ans=(a*ans);
                                                    a=(a*a);
                                                    b/=2;
                                                }
                                              
                                                return  ans;
                                        }
                                        public static long fib(long n){
                                            long[][]    f=new long[][]{{1L,1L},{1L,0}};
                                            if(n==0)
                                                return 0;
                                            f=arrpow(f,n-1);
                                            return f[0][0];
                                        }
                                        public static long[][] arrpow(long[][] a,long b){
                                           
                                                int n=a.length;
                                              //  long z=b;
                                                long[][] ans=new long[n][n];
                                                for(int i=0;i<n;i++)
                                                    ans[i][i]=1L;
                                                while(b>0){
                                                    
                                                    if(b%2==1)
                                                        ans=mul(a,ans);
                                                    a=mul(a,a);
                                                    b/=2;
                                                }
                                                
                                                return  ans;
                                        }
                                        public static long[][] mul(long[][] a,long[][] b){
                                            int n=a.length;
                                            int m=b[0].length;
                                            long[][] ans=new long[n][m];
                                            if(n==2 && m==2 && b.length==2){
                                                ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
                                                ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
                                                ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
                                                ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
                                                return ans;
             
                                            }
                                            for(int i=0;i<n;i++){
                                                for(int j=0;j<m;j++){
                                                    for(int k=0;k<b.length;k++){
                                                        ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                                                    }
                                                }
                                            }
                                            return ans; 
                                        }
                                         static class name implements Comparable<name> {
                                            long l,b,h;
                                            public name(long   x,long y,long z){
                                                {
                                                    l=x;
                                                    b=y;        
                                                }
                                                
                                                
                                                h=z;
                                            }
                                            public int compareTo(name o){
                                                return -(int)(l*b-o.l*o.b);
                                            }
                                            
                                        }
                                        public static class s {
                                            static BufferedReader reader;
                                            static StringTokenizer tokenizer;
                                        
                                            /** call this method to initialize reader for InputStream */
                                            static void init(InputStream input) {
                                                reader = new BufferedReader(
                                                            new InputStreamReader(input) );
                                                tokenizer = new StringTokenizer("");
                                            }   
                                        
                                            /** get next word */
                                            static String ns() throws IOException {
                                                while ( ! tokenizer.hasMoreTokens() ) {
                                                    //TODO add check for eof if necessary
                                                    tokenizer = new StringTokenizer(
                                                        reader.readLine() );
                                                }
                                                return tokenizer.nextToken();
                                            }
                                        
                                            static int ni() throws IOException {
                                                return Integer.parseInt( ns() );
                                            }
                                        
                                            static double nd() throws IOException {
                                                return Double.parseDouble( ns() );
                                            }
                                            static long nl() throws IOException {
                                                return Long.parseLong( ns() );
                                            }
                                        }
                                    }   