Problem: You are given a binary string s (each character of this string is either 0 or 1).

Let's denote the cost of string t as the number of occurences of s in t. For example, if s is 11 and t is 111011, then the cost of t is 3.

Let's also denote the Fibonacci strings sequence as follows:

  * F(0) is 0;
  * F(1) is 1;
  * F(i) = F(i - 1) + F(i - 2) if i > 1, where  +  means the concatenation of two strings.



Your task is to calculate the sum of costs of all subsequences of the string F(x). Since answer may be large, calculate it modulo 109 + 7.

Input

The first line contains two integers n and x (1 ≤ n ≤ 100, 0 ≤ x ≤ 100) — the length of s and the index of a Fibonacci string you are interested in, respectively.

The second line contains s — a string consisting of n characters. Each of these characters is either 0 or 1.

Output

Print the only integer — the sum of costs of all subsequences of the string F(x), taken modulo 109 + 7. 

Examples

Input

2 4
11


Output

14


Input

10 100
1010101010


Output

553403224

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class F implements Runnable{
	public static void main (String[] args) {new Thread(null, new F(), "_cf", 1 << 28).start();}

	int n, x, MOD = (int)1e9 + 7;
	String s;
	int[][][] dp;
	int[] pows = new int[101];
	
	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("Go!");

		pows[0] = pows[1] = 2;
		for(int i = 2; i < pows.length; i++)
			pows[i] = mult(pows[i - 1], pows[i - 2]);
		
		n = fs.nextInt();
		x = fs.nextInt();
		s = fs.next();
		dp = new int[n][n][x + 1];
		for(int i = 0; i < dp.length; i++)
			for(int j = 0; j < dp[i].length; j++)
				Arrays.fill(dp[i][j], -1);
		out.println(solve(0, n - 1, x));
		out.close();
	}
	
	int solve(int l, int r, int x) {
		if(x < 2) {
			if(l != r) return dp[l][r][x] = 0;
			if(s.charAt(l) - '0' == x) return dp[l][r][x] = 1;
			return dp[l][r][x] = 0;
		}
		int ret = dp[l][r][x];
		if(ret != -1) return ret;
		
		int res = 0;
		
		//the entire string is contained in F(x - 1) so we have 2^len(F(x-2)) options
		if(r == n - 1) res = add(res, mult(pows[x - 2], solve(l, r, x - 1)));
		else res = add(res, solve(l, r, x - 1));

		//the entire string is contained in F(x - 2) so we have 2^len(F(x-1)) options
		if(l == 0) res = add(res, mult(pows[x - 1], solve(l, r, x - 2)));
		else res = add(res, solve(l, r, x - 2));

		//occurrences of s[l,i] exactly once in all subsequences of F(x - 1)
		//multiplied with occurrences of s[i+1, r] exactly once in all subsequences
		//of F(x - 2)
		for(int i = l; i < r; i++) {
			res = add(res, mult(solve(l, i, x - 1), solve(i + 1, r, x - 2)));
		}
		return dp[l][r][x] = res;
	}
	
	int add(int a, int b) {
		a %= MOD;
		b %= MOD;
		a += b;
		a %= MOD;
		return a;
	}
	
	int mult(int a, int b) {
		a %= MOD;
		b %= MOD;
		long c = a;
		c *= b;
		c %= MOD;
		return (int)c;
	}
	
	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

}