There are b blocks of digits. Each one consisting of the same n digits, which are given to you in the input. Wet Shark must choose exactly one digit from each block and concatenate all of those digits together to form one large integer. For example, if he chooses digit 1 from the first block and digit 2 from the second block, he gets the integer 12. 

Wet Shark then takes this number modulo x. Please, tell him how many ways he can choose one digit from each block so that he gets exactly k as the final result. As this number may be too large, print it modulo 109 + 7.

Note, that the number of ways to choose some digit in the block is equal to the number of it's occurrences. For example, there are 3 ways to choose digit 5 from block 3 5 6 7 8 9 5 1 1 1 1 5.

Input

The first line of the input contains four space-separated integers, n, b, k and x (2 ≤ n ≤ 50 000, 1 ≤ b ≤ 109, 0 ≤ k < x ≤ 100, x ≥ 2) — the number of digits in one block, the number of blocks, interesting remainder modulo x and modulo x itself.

The next line contains n space separated integers ai (1 ≤ ai ≤ 9), that give the digits contained in each block.

Output

Print the number of ways to pick exactly one digit from each blocks, such that the resulting integer equals k modulo x.

Examples

Input

12 1 5 10
3 5 6 7 8 9 5 1 1 1 1 5


Output

3


Input

3 2 1 2
6 2 2


Output

0


Input

3 2 1 2
3 1 2


Output

6

Note

In the second sample possible integers are 22, 26, 62 and 66. None of them gives the remainder 1 modulo 2.

In the third sample integers 11, 13, 21, 23, 31 and 33 have remainder 1 modulo 2. There is exactly one way to obtain each of these integers, so the total answer is 6.
import java.util.*;
import java.io.*;
import java.math.*;
public class Main
{
    static class Reader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        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 String s(){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 long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;}
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;}
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = i();}return ret;}
    }
   
   
 
           //       |----|       /\      |    |   -----   |
           //       |   /       /  \     |    |     |     |
           //       |--/       /----\    |----|     |     |
           //       |   \     /      \   |    |     |     |
           //       |    \   /        \  |    |   -----   -------
 
    static long map[][];
    static int size;
    static long mod;
    public static long[][] expo(long pow)	
    {
		long ans[][]=new long[size][size];
		for(int i=0;i<size;i++)	
		ans[i][i]=1;
		while(pow!=0)
		{
			if((pow&1)!=0)	
			    ans=multiplyMatrix(ans, map);
			map=multiplyMatrix(map, map);
			pow/=2;
		}
		return ans;
	}
	public static long[][] multiplyMatrix(long m[][], long m2[][])	
	{
		long ans[][]=new long[size][size];
		for(int i=0;i<size;i++)
		for(int j=0;j<size;j++)
		{
			ans[i][j] =0;
			for(int k=0;k<size;k++)
			{
			    ans[i][j]+=m[i][k]*m2[k][j];
			    if(ans[i][j]>=mod)
			    ans[i][j]%=mod;
			}
		}
		return	ans;
	}
    public static void main(String[] args)throws IOException
    {
        PrintWriter out= new PrintWriter(System.out);
        Reader sc=new Reader();
        int n=sc.i(),b=sc.i(),k=sc.i(),x=sc.i();
        size=x;
        mod=1000000007;
        map=new long[size][size];
        int arr[]=sc.arr(n);
        for(int i=0;i<size;i++)
        {
            for(int j=0;j<n;j++)
            {
                map[i][(10*i+arr[j])%x]++;
            }
        }
        long ans[][]=expo(b);
        out.println(ans[0][k]);
        out.flush();
    }
}