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. 
//package learning;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class NitsLocal {
    static ArrayList<String> s1;
    static boolean[] prime;
    static int n = (int)1e7;
    
     static void sieve() {
Arrays.fill(prime	, true);
prime[0] = prime[1] = false;
for(int i = 2 ; i * i <= n ; ++i) {
if(prime[i]) {
for(int k = i * i; k<= n ; k+=i) {
prime[k] = false;
}
}
}
 
}
    public static void main(String[] args) {
        InputReader sc = new InputReader(System.in);
        n *= 2;
           prime  = new boolean[n + 1];
           //sieve();
                prime[1] = false;
              
                  
             /*    
        int n = sc.ni();
        int k = sc.ni();
        int []vis = new int[n+1];
        int []a = new int[k];
        for(int i=0;i<k;i++)
        {
            a[i] = i+1;
        }
        int j = k+1;
        int []b = new int[n+1];
        for(int i=1;i<=n;i++)
        {
            b[i] = -1;
        }
        int y = n - k +1;
        int tr = 0;
        int y1 = k+1;
        while(y-- > 0)
        {
        System.out.print("? ");
        for(int i=0;i<k;i++)
        {
            System.out.print(a[i] + " ");
        }
        
        System.out.flush();
        int pos = sc.ni();
        int a1 = sc.ni();
        b[pos] = a1;
        
        
        for(int i=0;i<k;i++)
        {
            if(a[i] == pos)
            {
                a[i] = y1;
                y1++;
            }
        }
        }
        ArrayList<Integer> a2 = new ArrayList<>();
        if(y >= k)
        {
            
        int c = 0;
        int k1 = 0;
            for(int i=1;i<=n;i++)
            {
                if(b[i] != -1)
                {
                    c++;
                    a[k1] = i;
                    a2.add(b[i]);
                    k1++;
                }
                if(c==k)
                    break;
            }
            
            Collections.sort(a2);
            System.out.print("? ");
        for(int i=0;i<k;i++)
        {
            System.out.print(a[i] + " ");
        }
        System.out.println();
        System.out.flush();
        int pos = sc.ni();
        int a1 = sc.ni();
        int ans = -1;
        for(int i=0;i<a2.size();i++)
        {
            if(a2.get(i) == a1)
            {
                ans = i+1;
                break;
            }
        }
        System.out.println("!" + " " + ans);
           System.out.flush();  
        }
        else
        {
            int k1 = 0;
            a = new int[k];
             for(int i=1;i<=n;i++)
            {
                if(b[i] != -1)
                {
                    
                    a[k1] = i;
                    a2.add(b[i]);
                    k1++;
                }
             
            }
              for(int i=1;i<=n;i++)
            {
                if(b[i] == -1)
                {
                    
                    a[k1] = i;
                    
                    k1++;
                    if(k1==k)
                        break;
                }
             
            }
              int ans = -1;
              while(true)
              {
                   System.out.print("? ");
                     for(int i=0;i<k;i++)
                   {
                         System.out.print(a[i] + " ");
                  }
                   System.out.println();
                   System.out.flush();
                   int pos = sc.ni();
                   int a1 = sc.ni();
                   int f = 0;
                   
                   if(b[pos] != -1)
                   {
                       Collections.sort(a2);
                       for(int i=0;i<a2.size();i++)
                       {
                           if(a2.get(i) == a1)
                           {
                               ans = i+1;
                               f = 1;
                               System.out.println("!" + " " + ans);
                               System.out.flush();
                               break;
                           }
                       }
                       if(f==1)
                           break;
                   }
                   else
                   {
                       b[pos] = a1;
                        a = new int[k];
                        a2.add(a1);
             for(int i=1;i<=n;i++)
            {
                if(b[i] != -1)
                {
                    
                    a[k1] = i;
                    a2.add(b[i]);
                    k1++;
                }
             
            }
              for(int i=1;i<=n;i++)
            {
                if(b[i] == -1)
                {
                    
                    a[k1] = i;
                    
                    k1++;
                    if(k1==k)
                        break;
                }
             
            }
                       
                   }
              }
        }  
          */
             /*
       int t = sc.ni();
             while(t-- > 0)
             {
                 int n = sc.ni();
                 int []a = sc.nia(n);
                 long sum = 0;
                 hm = new HashMap<>();
                 int d = 0;
                 for(int i=0;i<n;i++)
                 {
                     sum += (long) a[i];
                     if(sum < 0)
                     {
                         d = -1;
                     }
                     
                 }
                  l = 0;
                 r = 0;
                 f = 0;
                
                 long temp = maxSubArraySum(a,n,sum);
                 //w.println(temp + " " +f);
                
                if(f == -2)
                {
                   w.println("NO");
                }
                else
                {
                    w.println("YES");
                }
             }
               
           */
                 int t = sc.ni();
                 int x = sc.ni();
                 int []c = new int[400001];
                 int st = 0;
                 for(int i=0;i<t;i++)
                 {
                     int y = sc.ni();
                    // int req = (i)/x;
                     c[y%x]++;
                     int t1 = st;
                     while(c[t1%x] != 0)
                     {
                         int req = t1/x + 1;
                         if(c[t1%x] < req)
                         {
                             break;
                         }
                         else
                             t1++;
                         
                     }
                     w.println(t1);
                     st = t1;
                     
                 }
                    
                
             
                 
   
       w.close();
       
        
    }
   
   
 
     static int upperBound(ArrayList<Integer> a, int low, int high, int element){
    while(low < high){
        int middle = low + (high - low)/2;
        if(a.get(middle) > element)
            high = middle;
        else 
            low = middle + 1;
    }
    return low;
}
   static long func(long t,long e,long h,long a, long b)
   {
       if(e*a >= t)
           return t/a;
       else
       {
           return e + Math.min(h,(t-e*a)/b);
       }
   }
         
      
    public static int upperBound(int []arr,int n,int num)
    {
        int l = 0;
        int r = n;
        while(l < r)
        {
            int mid = (l+r)/2;
            if(num >= arr[mid])
            {
                l = mid +1;
            }
            else
                r = mid;
        }
        return l;
    }
    public static int countSetBits(int number){
        int count = 0;
        while(number>0){
            ++count;
            number &= number-1;
        }
        return count;
    }
    
     
      
 
    
    static HashSet<Integer> fac;
    public static void primeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
        int t = 0;
        while (n%2==0) 
        { 
            fac.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i*i <= n; i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                fac.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            fac.add(n);
    } 
     static long modexp(long x,long n,long M)
{
    long power = n;
    long result=1;
    x = x%M;
    while(power>0)
    {
        if(power % 2 ==1)
            result=(result * x)%M;
        x=(x*x)%M;
        power = power/2;
    }
    return result;
}
      static long modInverse(long A,long M)
{
    return modexp(A,M-2,M);
}
    static long gcd(long a,long b)
    {
        if(a==0)
            return b;
        else
            return gcd(b%a,a);
    }
    static class Temp{
        int a;
        int b;
        int c;
        int d;
      
        Temp(int a,int b,int c,int d)
        {
            this.a = a;
            this.b = b;
            this.c  =c;
            this.d = d;
            //this.d = d;
        }
    }
   
    
    
   static long sum1(int t1,int t2,int x,int []t)
   {
       int mid = (t2-t1+1)/2;
  if(t1==t2)
      return 0;
    
   else
   return sum1(t1,mid-1,x,t) + sum1(mid,t2,x,t);
    
     
   }
  
   
    static String replace(String s,int a,int n)
    {
        char []c = s.toCharArray();
        for(int i=1;i<n;i+=2)
        {
            int num = (int) (c[i] - 48);
            num += a;
            num%=10;
            c[i] = (char) (num+48);
        }
        return new String(c);
    }
    static String move(String s,int h,int n)
    {
        h%=n;
        char []c = s.toCharArray();
        char []temp = new char[n];
        for(int i=0;i<n;i++)
        {
            temp[(i+h)%n] = c[i];
        }
        return new String(temp);
    }
    
     public static int ip(String s){
return Integer.parseInt(s);
}
     static class multipliers implements Comparator<Long>{
  
         
  public int compare(Long a,Long b) {
   if(a<b)
    return 1;
   else if(b<a)
    return -1;
   else
    return 0;
  }
 }
     
     static class multipliers1 implements Comparator<Student>{
  
  public int compare(Student a,Student b) {
   if(a.id<b.id)
    return -1;
   else if(b.id<a.id)
    return 1;
   else
   {
       if(a.b < b.b)
           return -1;
       else if(b.b<a.b)
           return 1;
       else
           return 0;
           
    //return 0;
   }
  }

 }

    // Java program to generate power set in 
// lexicographic order. 
 
    
    
    
      static class InputReader {
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
 
public InputReader(InputStream st) {
this.stream = st;
}
 
public int read() {
if (snumChars == -1)
throw new InputMismatchException();
if (curChar >= snumChars) {
curChar = 0;
try {
snumChars = stream.read(buf);
} catch (IOException e) {
throw new InputMismatchException();
}
if (snumChars <= 0)
return -1;
}
return buf[curChar++];
}
 
public int ni() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
int res = 0;
do {
res *= 10;
res += c - '0';
c = read();
} while (!isSpaceChar(c));
return res * sgn;
}
 
public long nl() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
long res = 0;
do {
res *= 10;
res += c - '0';
c = read();
} while (!isSpaceChar(c));
return res * sgn;
}
 
public int[] nia(int n) {
int a[] = new int[n];
for (int i = 0; i < n; i++) {
a[i] = ni();
}
return a;
}
 
public String rs() {
int c = read();
while (isSpaceChar(c)) {
c = read();
}
StringBuilder res = new StringBuilder();
do {
res.appendCodePoint(c);
c = read();
} while (!isSpaceChar(c));
return res.toString();
}
 
public String nextLine() {
int c = read();
while (isSpaceChar(c))
c = read();
StringBuilder res = new StringBuilder();
do {
res.appendCodePoint(c);
c = read();
} while (!isEndOfLine(c));
return res.toString();
}
 
public boolean isSpaceChar(int c) {
return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
 
private boolean isEndOfLine(int c) {
return c == '\n' || c == '\r' || c == -1;
}
 
}
 
 
 
 
 
   
static PrintWriter w = new PrintWriter(System.out);
                  static class Student
    {
        int id;
        //int x;
       
       int b;
      
        //long z;
        
        Student(int id,int b)
        {
            this.id = id;
            //this.x = x;
            //this.s = s;
            this.b = b;
          
           // this.z = z;
            
            
            
           
        }
        
    }
}