Anton likes to listen to fairy tales, especially when Danik, Anton's best friend, tells them. Right now Danik tells Anton a fairy tale:

"Once upon a time, there lived an emperor. He was very rich and had much grain. One day he ordered to build a huge barn to put there all his grain. Best builders were building that barn for three days and three nights. But they overlooked and there remained a little hole in the barn, from which every day sparrows came through. Here flew a sparrow, took a grain and flew away..."

More formally, the following takes place in the fairy tale. At the beginning of the first day the barn with the capacity of n grains was full. Then, every day (starting with the first day) the following happens:

  * m grains are brought to the barn. If m grains doesn't fit to the barn, the barn becomes full and the grains that doesn't fit are brought back (in this problem we can assume that the grains that doesn't fit to the barn are not taken into account). 
  * Sparrows come and eat grain. In the i-th day i sparrows come, that is on the first day one sparrow come, on the second day two sparrows come and so on. Every sparrow eats one grain. If the barn is empty, a sparrow eats nothing. 



Anton is tired of listening how Danik describes every sparrow that eats grain from the barn. Anton doesn't know when the fairy tale ends, so he asked you to determine, by the end of which day the barn will become empty for the first time. Help Anton and write a program that will determine the number of that day!

Input

The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018) — the capacity of the barn and the number of grains that are brought every day.

Output

Output one integer — the number of the day when the barn will become empty for the first time. Days are numbered starting with one.

Examples

Input

5 2


Output

4


Input

8 1


Output

5

Note

In the first sample the capacity of the barn is five grains and two grains are brought every day. The following happens:

  * At the beginning of the first day grain is brought to the barn. It's full, so nothing happens. 
  * At the end of the first day one sparrow comes and eats one grain, so 5 - 1 = 4 grains remain. 
  * At the beginning of the second day two grains are brought. The barn becomes full and one grain doesn't fit to it. 
  * At the end of the second day two sparrows come. 5 - 2 = 3 grains remain. 
  * At the beginning of the third day two grains are brought. The barn becomes full again. 
  * At the end of the third day three sparrows come and eat grain. 5 - 3 = 2 grains remain. 
  * At the beginning of the fourth day grain is brought again. 2 + 2 = 4 grains remain. 
  * At the end of the fourth day four sparrows come and eat grain. 4 - 4 = 0 grains remain. The barn is empty. 



So the answer is 4, because by the end of the fourth day the barn becomes empty.
 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 long ct=0;
                                static int sid,tt;
                                static int[] tin,tout,parent,level;
                                static HashMap<Long,Integer> hm;
                                static long[] dp1,dp2,dp3,dp4;
                                public static void main(String[] args)  throws IOException {
                                    ///long start=System.currentTimeMillis();
                                    boolean online =false;
                                    String fileName = "code";
                                    PrintWriter out; 
                                    if (online) {
                                        s.init(new FileInputStream(new File(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

                                   long n=s.nl();
                                   long m=s.nl();
                                   

                                   if(m<n){

                                        long ans=0;
                                        long l=1;
                                        long h=n;
                                        BigInteger a=new BigInteger(n+"");
                                        BigInteger b=new BigInteger(m+"");
                                        BigInteger c=new BigInteger("3");
                                        BigInteger d=new BigInteger("2");
                                        while(l<h){
                                            long mid=(l+h)/2;
                                            BigInteger z=new BigInteger(mid+"");
                                            BigInteger w=z.multiply(z);
                                            w=((w.add(z.multiply(c)).add(d.multiply(b))).add(d)).subtract((a.multiply(d)));
                                            if(w.compareTo(new BigInteger("0"))<0){
                                                l=mid+1;
                                            }
                                            else
                                                h=mid;
                                        }
                                        //out.println(l);
                                        out.println(Math.min(n,l+m+1));
                                    }
                                    else
                                        out.println((long)n);

                                   out.close();
                     
                                }
                                                      //   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, 0.00000000000001);
                                }
                                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 ;
                                    int time;
                                    public item(int x,int y){
                                        id=x;
                                        time=y;
                                    }
                                    public int compareTo(item o){
                                       return time-o.time;
                                    }
                                    
                                }
                               
                                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() );
                                    }
                                }
                            }  
