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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author palayutm
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        ProblemFFibonacciStringSubsequences solver = new ProblemFFibonacciStringSubsequences();
        solver.solve(1, in, out);
        out.close();
    }

    static class ProblemFFibonacciStringSubsequences {
        int mod = (int) 1e9 + 7;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt(), X = in.nextInt();
            String s = in.next();
            long[][][] f = new long[Math.max(2, X + 1)][s.length()][s.length()];
            for (int i = 0; i < s.length(); i++) {
                f[s.charAt(i) - '0'][i][i] = 1;
            }
            int[] fib = new int[Math.max(2, X + 1)];
            fib[0] = fib[1] = 1;
            for (int i = 2; i <= X; i++) {
                fib[i] = (fib[i - 2] + fib[i - 1]) % (mod - 1);
            }
            for (int i = 2; i <= X; i++) {
                for (int L = 0; L < s.length(); L++) {
                    for (int R = 0; R < s.length(); R++) {
                        f[i][L][R] = (L == 0 ? IntegerUtils.powMod(2, fib[i - 1], mod) : 1) * f[i - 2][L][R];
                        f[i][L][R] += (R == s.length() - 1 ? IntegerUtils.powMod(2, fib[i - 2], mod) : 1) * f[i - 1][L][R];
                        f[i][L][R] %= mod;
                        for (int m = L; m < R; m++) {
                            f[i][L][R] = (f[i][L][R] + f[i - 1][L][m] * f[i - 2][m + 1][R]) % mod;
                        }
                    }
                }
            }
            out.println(f[X][0][s.length() - 1]);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class IntegerUtils {
        public static long powMod(long x, long y, int mod) {
            long ret = 1;
            x %= mod;
            while (y > 0) {
                if (y % 2 > 0) {
                    ret = ret * x % mod;
                }
                x = x * x % mod;
                y >>= 1;
            }
            return ret;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream out) {
            super(out);
        }

        public OutputWriter(Writer out) {
            super(out);
        }

        public void close() {
            super.close();
        }

    }
}