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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int dx44[5] = {0, -1, -1, 1, 1};
const int dy44[5] = {0, -1, 1, -1, 1};
const int dx4[5] = {0, -1, 0, 1, 0};
const int dy4[5] = {0, 0, 1, 0, -1};
const int dx8[9] = {0, -1, 0, 1, 0, 1, 1, -1, -1};
const int dy8[9] = {0, 0, 1, 0, -1, 1, -1, 1, -1};
const int maxn = 2e5 + 50;
const double PI = acos(-1.0);
const long long mod = 1e9 + 7;
long long po(long long a, long long b, long long mod) {
  long long res = 1;
  a %= mod;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
  }
  return res;
}
long long gcd(long long a, long long b) {
  if (a == 0) {
    return b;
  } else {
    return gcd(b % a, a);
  }
}
void YES() {
  puts("YES");
  exit(0);
}
void Yes() { puts("Yes"); }
void NO() {
  puts("NO");
  exit(0);
}
void No() { puts("No"); }
void one() {
  puts("-1");
  exit(0);
}
long long n, x;
char val[105];
long long dp[105][105][105];
long long f[105] = {2, 2};
void solve() {
  scanf("%lld", &(n)), scanf("%lld", &(x));
  scanf("%s", val + 1);
  for (int i = 1; i <= n; i++) {
    dp[val[i] - '0'][i][i] = 1;
  }
  for (int i = 2; i <= x; i++) {
    f[i] = f[i - 1] * f[i - 2] % mod;
    for (int le = 1; le <= n; le++) {
      for (int ri = le; ri <= n; ri++) {
        dp[i][le][ri] += dp[i - 1][le][ri] * (ri == n ? f[i - 2] : 1);
        dp[i][le][ri] %= mod;
        dp[i][le][ri] += dp[i - 2][le][ri] * (le == 1 ? f[i - 1] : 1);
        dp[i][le][ri] %= mod;
        for (int m = le; m <= ri - 1; m++) {
          dp[i][le][ri] += (dp[i - 1][le][m] * dp[i - 2][m + 1][ri]) % mod;
          dp[i][le][ri] %= mod;
        }
      }
    }
  }
  printf("%lld\n", dp[x][1][n]);
}
int main() {
  solve();
  return 0;
}