Recall that MEX of an array is a minimum non-negative integer that does not belong to the array. Examples:

  * for the array [0, 0, 1, 0, 2] MEX equals to 3 because numbers 0, 1 and 2 are presented in the array and 3 is the minimum non-negative integer not presented in the array; 
  * for the array [1, 2, 3, 4] MEX equals to 0 because 0 is the minimum non-negative integer not presented in the array; 
  * for the array [0, 1, 4, 3] MEX equals to 2 because 2 is the minimum non-negative integer not presented in the array. 



You are given an empty array a=[] (in other words, a zero-length array). You are also given a positive integer x.

You are also given q queries. The j-th query consists of one integer y_j and means that you have to append one element y_j to the array. The array length increases by 1 after a query.

In one move, you can choose any index i and set a_i := a_i + x or a_i := a_i - x (i.e. increase or decrease any element of the array by x). The only restriction is that a_i cannot become negative. Since initially the array is empty, you can perform moves only after the first query.

You have to maximize the MEX (minimum excluded) of the array if you can perform any number of such operations (you can even perform the operation multiple times with one element).

You have to find the answer after each of q queries (i.e. the j-th answer corresponds to the array of length j).

Operations are discarded before each query. I.e. the array a after the j-th query equals to [y_1, y_2, ..., y_j].

Input

The first line of the input contains two integers q, x (1 ≤ q, x ≤ 4 ⋅ 10^5) — the number of queries and the value of x.

The next q lines describe queries. The j-th query consists of one integer y_j (0 ≤ y_j ≤ 10^9) and means that you have to append one element y_j to the array.

Output

Print the answer to the initial problem after each query — for the query j print the maximum value of MEX after first j queries. Note that queries are dependent (the array changes after each query) but operations are independent between queries.

Examples

Input


7 3
0
1
2
2
0
0
10


Output


1
2
3
3
4
4
7


Input


4 3
1
2
1
2


Output


0
0
0
0

Note

In the first example:

  * After the first query, the array is a=[0]: you don't need to perform any operations, maximum possible MEX is 1. 
  * After the second query, the array is a=[0, 1]: you don't need to perform any operations, maximum possible MEX is 2. 
  * After the third query, the array is a=[0, 1, 2]: you don't need to perform any operations, maximum possible MEX is 3. 
  * After the fourth query, the array is a=[0, 1, 2, 2]: you don't need to perform any operations, maximum possible MEX is 3 (you can't make it greater with operations). 
  * After the fifth query, the array is a=[0, 1, 2, 2, 0]: you can perform a[4] := a[4] + 3 = 3. The array changes to be a=[0, 1, 2, 2, 3]. Now MEX is maximum possible and equals to 4. 
  * After the sixth query, the array is a=[0, 1, 2, 2, 0, 0]: you can perform a[4] := a[4] + 3 = 0 + 3 = 3. The array changes to be a=[0, 1, 2, 2, 3, 0]. Now MEX is maximum possible and equals to 4. 
  * After the seventh query, the array is a=[0, 1, 2, 2, 0, 0, 10]. You can perform the following operations: 
    * a[3] := a[3] + 3 = 2 + 3 = 5, 
    * a[4] := a[4] + 3 = 0 + 3 = 3, 
    * a[5] := a[5] + 3 = 0 + 3 = 3, 
    * a[5] := a[5] + 3 = 3 + 3 = 6, 
    * a[6] := a[6] - 3 = 10 - 3 = 7, 
    * a[6] := a[6] - 3 = 7 - 3 = 4. 
The resulting array will be a=[0, 1, 2, 5, 3, 6, 4]. Now MEX is maximum possible and equals to 7. 
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.*; 
import java.util.StringTokenizer; 
import java.io.PrintWriter;
import java.io.*;
import java.util.stream.Collectors.*;
import java.lang.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;
public class Ideo
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
   
static int power(int x,int y) 
{ 
    int res = 1;      // Initialize result 
  
      // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y%2==1) 
            res = (res*x); 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x);   
    } 
    return res; 
} 
 
 static long gcd(long a,long b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
 
 
  static boolean compareSeq(char[] S, int x, int y, int n) 
    { 
        for (int i = 0; i < n; i++)
         {
 
            if (S[x] < S[y]) 
               return true;
            else if (S[x] > S[y]) 
                return false; 
            x = (x + 1) % n; 
            y = (y + 1) % n; 
        } 
        return true; 
    } 
 
    static void build(long[] sum,int[] arr,int n)
    {
      for(int i=0;i<(1<<n);i++)
      {
        long total=0;
        for(int j=0;j<n;j++)
        {
          if((i & (1 << j)) > 0)
            total+=arr[j];
        }
 
        sum[i]=total;
      }
    }

 
       static int parity(int a)
       {
    a^=a>>16;
    a^=a>>8;
    a^=a>>4;
    a^=a>>2;
    a^=a>>1;
    return a&1;
  }
/*
  PriorityQueue<aksh> pq = new PriorityQueue<>((o1, o2) -> {
            if (o1.p < o2.p)
                return 1;
            else if (o1.p > o2.p)
                return -1;
            else
                return 0;
 
        });//decreasing order acc to p*/
static int power(int x, int y, int m)  
    { 
        if (y == 0) 
            return 1; 
          
        int p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
/*static int modinv(int a, int m) 
    { 
        int g = gcd(a, m); 
        if (g != 1) 
            return 0;
        else 
        { 
           return power(a, m - 2, m); 
        } 
        //return 0;
    } */
 
static int[] product(int[] nums) {
    int[] result = new int[nums.length];
 
    int[] t1 = new int[nums.length];
    int[] t2 = new int[nums.length];
 
    t1[0]=1;
    t2[nums.length-1]=1;
 
    //scan from left to right
    for(int i=0; i<nums.length-1; i++){
        t1[i+1] = nums[i] * t1[i];
    }
 
    //scan from right to left
    for(int i=nums.length-1; i>0; i--){
        t2[i-1] = t2[i] * nums[i];
    }
 
    for(int i=0;i<nums.length;i++)
      {
        System.out.print(t1[i]+" "+t2[i]);
        System.out.println();
      }
 
    //multiply
    for(int i=0; i<nums.length; i++){
        result[i] = t1[i] * t2[i];
    }
 
    return result;
}
 
static int getsum(int[] bit,int ind)
{
  int sum=0;
  while(ind>0)
  {
    sum+=bit[ind];
    ind-= ind & (-ind);
  }
 
  return sum;
}
 
static void update(int[] bit,int max,int ind,int val)
{
  while(ind<=max)
  {
    bit[ind]+=val;
    ind+= ind & (-ind);
  }
}
 
    //static ArrayList<Integer>[] adj;
 
    static boolean check(long mid,long a,long b)
    {
      long count=1;
      while(count<=mid)
      {
        count++;
        if(a<b)
          a+=count;
        else
          b+=count;
 
        if(a==b)
          return true;
      }
        return false;
    }
 
    static class aksh implements Comparable<aksh>
    {
      int x;
      int y;
 
      public aksh(int x,int y)
      {
        this.x=x;
        this.y=y;
      }
 
      public int compareTo(aksh o)
      {
        if(x!=o.x)
          return x-o.x;
        else
          return y-o.y;
      }
    }
    static int get(int arr[], int n) 
    { 
        int result = 0; 
        int x, sum; 
          
        // Iterate through every bit 
        for(int i=0; i<32; i++) 
        { 
            // Find sum of set bits at ith position in all  
            // array elements 
            sum = 0; 
            x = (1 << i); 
            for(int j=0; j<n; j++) 
            { 
                if((arr[j] & x)!=0) 
                sum++; 
            } 
            // The bits with sum not multiple of 3, are the 
            // bits of element with single occurrence. 
            if ((sum % 3)!=0) 
            result |= x; 
        } 
        return result; 
    } 
    /*        Collections.sort(orders, new Comparator<Point>() {
            @Override
            public int compare(Point o1, Point o2) {
                if (o1.diff < o2.diff) {
                    return -1;
                } else if (o1.diff > o2.diff) {
                    return 1;
                } else {
                    return 0;
                }
            }
        });  */
 
 
    static boolean isPrime(int n)  
    {  
        // Corner cases  
        if (n <= 1) return false;  
        if (n <= 3) return true;  
          
        // This is checked so that we can skip  
        // middle five numbers in below loop  
        if (n % 2 == 0 || n % 3 == 0) return false;  
          
        for (int i = 5; i * i <= n; i = i + 6)  
            if (n % i == 0 || n % (i + 2) == 0)  
            return false;  
          
        return true;  
    }  
      
    static int nextPrime(int N)  
    {  
      
        // Base case  
        if (N <= 1)  
            return (2-N);  
      
        int prime = N;  
        boolean found = false;  
      
        // Loop continuously until isPrime returns  
        // true for a number greater than n  
        while (!found)  
        {  
            if (isPrime(prime))  
                {
                  found = true;
                  break;
                }  
 
            prime++;
        }  
      
        return (prime-N);  
    }  
 
 
    static long product(long x) 
{ 
    long prod = 1; 
    while (x > 0)  
    { 
        prod *= (x % 10); 
        x /= 10; 
    } 
    return prod; 
} 
  
// This function returns the number having 
// maximum product of the digits 
static long findNumber(long l, long r) 
{ 
    // Converting both integers to strings 
    //string a = l.ToString(); 
    String b = Long.toString(r); 
  
    // Let the current answer be r 
    long ans = r; 
    for (int i = 0; i < b.length(); i++)  
    { 
        if (b.charAt(i) == '0') 
            continue; 
  
        // Stores the current number having 
        // current digit one less than current 
        // digit in b 
        char[] curr = b.toCharArray(); 
        curr[i] = (char)(((int)(curr[i] -  
                    (int)'0') - 1) + (int)('0')); 
  
        // Replace all following digits with 9 
        // to maximise the product 
        for (int j = i + 1; j < curr.length; j++) 
            curr[j] = '9'; 
  
        // Convert string to number 
        int num = 0; 
        for (int j = 0; j < curr.length; j++) 
            num = num * 10 + (curr[j] - '0'); 
  
        // Check if it lies in range and its product 
        // is greater than max product 
        if (num >= l && product(ans) < product(num)) 
            ans = num; 
    } 
  
    return product(ans); 
} 
 
static long mod=998244353;
 
static long pow(long in, long pow) {
    if(pow == 0) return 1;
    long out = pow(in, pow / 2);
    out = (out * out) % mod;
    if(pow % 2 == 1) out = (out * in) % mod;
    return out;
  }
  static long inv(long in) {
    return pow(in, mod - 2);
  }
 
  static void swap(int x,int y)
  {
    int temp=x;
    x=y;
    y=temp;
  }
 
  static int[] par;
  static int[] size;
  static int find(int i) 
  {
     if (par[i] == i)
      return i;
 
    return par[i] = find(par[par[i]]);
  }
 
  static void union(int x, int y) 
  {
      x = find(x);
      y = find(y);
      if (x == y)
        return;
      if (size[x] < size[y])
        swap(x, y);
 
      par[y] = x;
      size[x] += size[y];
    }
 
 
    static void multisourcebfs(long[] arr,int n,int m)
    {
      //HashSet<Long> vis=new HashSet<>();
      HashMap<Long,Long> dis=new HashMap<>();
      Queue<Long> q=new LinkedList<>();
 
      for(int i=0;i<arr.length;i++)
      {
        dis.put(arr[i],(long)0);
        q.add(arr[i]);
        //vis.add(arr[i]);
      }
 
      long[] res=new long[m];
      long ans=0;
      int k=0;
      while(!q.isEmpty())
      {
        if(k==m)
          break;
        long x=q.remove();
        if(dis.get(x)!=0)
        {
          ans+=dis.get(x);
          res[k]=x;
          k++;
        }
 
        if(dis.get(x-1)==null)
        {
          dis.put(x-1, dis.get(x)+1);
          q.add(x-1);
          //vis.add(x-1);
        }
 
        if(dis.get(x+1)==null)
        {
          dis.put(x+1, dis.get(x)+1);
          q.add(x+1);
          //vis.add(x+1);
        }
      }
 
      System.out.println(ans);
 
      for(int i=0;i<m;i++)
        System.out.print(res[i]+" ");
 
    }
 
    static int x; 
    static int maxcount=0;
    static void dfs(int node,int par,int dist)
    {
        if(dist>=maxcount)
        {
           maxcount=dist;
           x=node;
        }
 
        List<Integer> l = adj[node]; 
        for(Integer i: l)
        {
          if(i!=par)
          dfs(i,node,dist+1);
        }
    }

    

    static int h;
    static int w;
    static int bfs(char[][] ch,int i,int j)
    {
        Queue<aksh> q=new LinkedList<>();
        q.add(new aksh(i,j));

        int[][] dis=new int[h][w];
        int[][] vis=new int[h][w];
        vis[i][j]=1;
        dis[i][j]=0;
 
        while(!q.isEmpty())
        {
          aksh arr=q.poll();
          int x1=arr.x;
          int y1=arr.y;
 
          if((x1-1)>=0 && ch[x1-1][y1]!='#' && vis[x1-1][y1]==0)
          {
            vis[x1-1][y1]=1;
            q.add(new aksh(x1-1, y1));
            dis[x1-1][y1]=Math.max(dis[x1-1][y1],dis[x1][y1]+1);
          }
 
          if((x1+1)<h && ch[x1+1][y1]!='#' && vis[x1+1][y1]==0)
          {
            vis[x1+1][y1]=1;
            dis[x1+1][y1]=Math.max(dis[x1+1][y1],dis[x1][y1]+1);
            q.add(new aksh(x1+1, y1));
          }
 
          if((y1-1)>=0 && ch[x1][y1-1]!='#' && vis[x1][y1-1]==0)
          {
            vis[x1][y1-1]=1;
            dis[x1][y1-1]=Math.max(dis[x1][y1-1],dis[x1][y1]+1);
            q.add(new aksh(x1,y1-1));
          }
 
    
          if((y1+1)<w && ch[x1][y1+1]!='#' && vis[x1][y1+1]==0)
          {
            vis[x1][y1+1]=1;
            dis[x1][y1+1]=Math.max(dis[x1][y1+1],dis[x1][y1]+1);
            q.add(new aksh(x1,y1+1));
          }
        }
        int max=Integer.MIN_VALUE;

        for(int x=0;x<h;x++)
        {
          for(int y=0;y<w;y++)
            max=Math.max(dis[x][y],max);
        }

        return max;
    }

    static ArrayList<Integer> cnt;

    static void primefact(int n)
    {
 
          for (int i=2;i*i<=n;i++)
           {
              while ((n % i)==0)
              {
                cnt.add(i);
                n /= i;
              }
           }

          if(n>1)
             {
              cnt.add(n);
             }
    }

    static final long INF = Long.MAX_VALUE/5;
    static ArrayList<Integer>[] adj;
    public static void main(String args[] ) throws Exception 
    {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT */
 
        FastReader sc=new FastReader();
        int q=sc.nextInt();
        int x=sc.nextInt();
        int[] c=new int[x];
        int ans=0;

        while(q-->0)
        {

          //int[] temp=new int[x];
         // int[] used=new int[x];
          int y=sc.nextInt();
          y%=x;

          c[y]++;
          while(c[ans%x]>0)
            {
              c[ans%x]--;
              ans++;
            }

          System.out.println(ans);

        }









         


        
       
        
        }
 
    }
 