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.*;

/**
 * Created by dalt on 2018/3/25.
 */
public class CF946F {
    public static BlockReader input;
    public static PrintStream output;
    public static void main(String[] args) throws FileNotFoundException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            input = new BlockReader(new FileInputStream("D:\\DataBase\\TESTCASE\\codeforces\\CF946F.in"));
            output = System.out;
        }else{
            input = new BlockReader(System.in);
            output = new PrintStream(new BufferedOutputStream(System.out), false);
        }

        solve();

        output.flush();
    }

    public static void solve() {
        int n = input.nextInteger();
        int x = input.nextInteger();
        String s = input.nextBlock();
        int slen = s.length();
        final long MOD = 1000000007;
        final int ALIGN_LEFT = 0;
        final int ALIGN_RIGHT = 1;
        final int ALIGN_CENTER = 2;
        final int ALIGN_LEFT_RIGHT = 3;

        long[][][][] dp = new long[Math.max(x + 1, 2)][slen + 1][slen + 1][4];
        long[] lengthes = new long[101];
        lengthes[0] = lengthes[1] = 1;

        for (int j = 0, bound = 2; j < bound; j++) {
            for (int i = 0; i <= slen; i++) {
                for (int k = 0; k < 4; k++) {
                    dp[j][i][i][ALIGN_LEFT] = 2;
                    dp[j][i][i][ALIGN_RIGHT] = 2;
                    dp[j][i][i][ALIGN_CENTER] = 2;
                    dp[j][i][i][ALIGN_LEFT_RIGHT] = 1;
                }
            }
        }

        for (int i = 0; i < slen; i++) {
            int c = s.charAt(i) - '0';
            dp[c][i][i + 1][ALIGN_LEFT] = 1;
            dp[c][i][i + 1][ALIGN_RIGHT] = 1;
            dp[c][i][i + 1][ALIGN_CENTER] = 1;
            dp[c][i][i + 1][ALIGN_LEFT_RIGHT] = 1;
        }

        for (int i = 2; i <= x; i++) {
            int last = i - 1;
            int last2 = i - 2;
            lengthes[i] = (lengthes[last] + lengthes[last2]) % (MOD - 1);

            long pLast = pow(2, lengthes[last], MOD);
            long pLast2 = pow(2, lengthes[last2], MOD);
            for (int j = 0; j <= slen; j++) {
                dp[i][j][j][ALIGN_LEFT] = pLast * pLast2 % MOD;
                dp[i][j][j][ALIGN_RIGHT] = dp[i][j][j][ALIGN_LEFT];
                dp[i][j][j][ALIGN_CENTER] = dp[i][j][j][ALIGN_LEFT];
                dp[i][j][j][ALIGN_LEFT_RIGHT] = 1;
                for (int k = j + 1; k <= slen; k++) {
                    dp[i][j][k][ALIGN_LEFT] = (dp[last][j][k][ALIGN_LEFT] * pLast2 + dp[last2][j][k][ALIGN_LEFT]) % MOD;
                    dp[i][j][k][ALIGN_RIGHT] = (dp[last][j][k][ALIGN_RIGHT] + pLast * dp[last2][j][k][ALIGN_RIGHT]) % MOD;
                    dp[i][j][k][ALIGN_CENTER] = (dp[last][j][k][ALIGN_CENTER] * pLast2 + pLast * dp[last2][j][k][ALIGN_CENTER]) % MOD;
                    dp[i][j][k][ALIGN_LEFT_RIGHT] = (dp[last][j][k][ALIGN_LEFT_RIGHT] + dp[last2][j][k][ALIGN_LEFT_RIGHT]) % MOD;
                    for (int sep = j + 1; sep < k; sep++) {
                        dp[i][j][k][ALIGN_LEFT] = (dp[i][j][k][ALIGN_LEFT] + dp[last][j][sep][ALIGN_LEFT_RIGHT] * dp[last2][sep][k][ALIGN_LEFT]) % MOD;
                        dp[i][j][k][ALIGN_RIGHT] = (dp[i][j][k][ALIGN_RIGHT] + dp[last][j][sep][ALIGN_RIGHT] * dp[last2][sep][k][ALIGN_LEFT_RIGHT]) % MOD;
                        dp[i][j][k][ALIGN_LEFT_RIGHT] = (dp[i][j][k][ALIGN_LEFT_RIGHT] + dp[last][j][sep][ALIGN_LEFT_RIGHT] * dp[last2][sep][k][ALIGN_LEFT_RIGHT]) % MOD;
                        dp[i][j][k][ALIGN_CENTER] = (dp[i][j][k][ALIGN_CENTER] + dp[last][j][sep][ALIGN_RIGHT] * dp[last2][sep][k][ALIGN_LEFT]) % MOD;
                    }
                }
            }
        }

         System.out.println(dp[x][0][slen][ALIGN_CENTER]);
    }

    public static long pow(long x, long n, long MOD) {
        int bit = 31;
        for (; bit >= 0 && (n & (1 << bit)) == 0; bit--) ;
        long product = 1;
        for (; bit >= 0; bit--) {
            product = (product * product) % MOD;
            if ((n & (1 << bit)) != 0) {
                product = (product * x) % MOD;
            }
        }
        return (int) product;
    }

    public static class BlockReader {
        static final int EOF = -1;
        InputStream is;
        byte[] dBuf;
        int dPos, dSize, next;
        StringBuilder builder = new StringBuilder();

        public BlockReader(InputStream is) {
            this(is, 4096);
        }

        public BlockReader(InputStream is, int bufSize) {
            this.is = is;
            dBuf = new byte[bufSize];
            next = nextByte();
        }

        public int nextByte() {
            while (dPos >= dSize) {
                if (dSize == -1) {
                    return EOF;
                }
                dPos = 0;
                try {
                    dSize = is.read(dBuf);
                } catch (Exception e) {
                }
            }
            return dBuf[dPos++];
        }

        public String nextBlock() {
            builder.setLength(0);
            skipBlank();
            while (next != EOF && !Character.isWhitespace(next)) {
                builder.append((char) next);
                next = nextByte();
            }
            return builder.toString();
        }

        public void skipBlank() {
            while (Character.isWhitespace(next)) {
                next = nextByte();
            }
        }

        public int nextInteger() {
            skipBlank();
            int ret = 0;
            boolean rev = false;
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = nextByte();
            }
            while (next >= '0' && next <= '9') {
                ret = (ret << 3) + (ret << 1) + next - '0';
                next = nextByte();
            }
            return rev ? -ret : ret;
        }

        public int nextBlock(char[] data, int offset) {
            skipBlank();
            int index = offset;
            int bound = data.length;
            while (next != EOF && index < bound && !Character.isWhitespace(next)) {
                data[index++] = (char) next;
                next = nextByte();
            }
            return index - offset;
        }

        public boolean hasMore() {
            skipBlank();
            return next != EOF;
        }
    }
}