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;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T, class T1>
inline void gn(T &first, T1 &second) {
  gn(first);
  gn(second);
}
template <class T, class T1, class T2>
inline void gn(T &first, T1 &second, T2 &z) {
  gn(first);
  gn(second);
  gn(z);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
inline unsigned int myrand(int n) {
  unsigned int u = rand() % n;
  int c = rand() % 10;
  u ^= u << c;
  u ^= (u << 7) & 263692864;
  u ^= (u << 15) & 402273075;
  u %= n;
  return u;
}
char s[111];
long long len[111];
int mlen[111];
int ans[111][111][111];
int cnt[111][3][111][111];
int cflag[111][3][111][111];
int flag[111][111][111];
int calc(int first, int k, int st, int ed) {
  if (cflag[first][k][st][ed]) return cnt[first][k][st][ed];
  if (first == 0) {
    if (s[st] == '0' and ed == st + 1)
      return 1;
    else
      return 0;
  }
  if (first == 1) {
    if (s[st] == '1' and ed == st + 1)
      return 1;
    else
      return 0;
  }
  int res;
  if (k == 0) {
    res = (long long)calc(first - 1, k, st, ed) *
          power(2, mlen[first - 2], 1000000007) % 1000000007;
    res += calc(first - 2, k, st, ed);
    res %= 1000000007;
    for (int i = st + 1; i < ed; i++) {
      res += 1ll * calc(first - 1, 2, st, i) * calc(first - 2, 0, i, ed) %
             1000000007;
      res %= 1000000007;
    }
  }
  if (k == 1) {
    res = (long long)calc(first - 2, k, st, ed) *
          power(2, mlen[first - 1], 1000000007) % 1000000007;
    res += calc(first - 1, k, st, ed);
    res %= 1000000007;
    for (int i = st + 1; i < ed; i++) {
      res += 1ll * calc(first - 2, 2, i, ed) * calc(first - 1, 1, st, i) %
             1000000007;
      res %= 1000000007;
    }
  }
  if (k == 2) {
    res = 0;
    res += calc(first - 2, 2, st, ed);
    res += calc(first - 1, 2, st, ed);
    res %= 1000000007;
    for (int i = st + 1; i < ed; i++) {
      res += 1ll * calc(first - 1, 2, st, i) * calc(first - 2, 2, i, ed) %
             1000000007;
      res %= 1000000007;
    }
  }
  cflag[first][k][st][ed] = 1;
  return cnt[first][k][st][ed] = res;
}
int solve(int first, int st, int ed) {
  if (len[first] < ed - st) return 0;
  if (flag[first][st][ed]) return ans[first][st][ed];
  if (first == 0) {
    if (s[st] == '0')
      return 1;
    else
      return 0;
  }
  if (first == 1) {
    if (s[st] == '1')
      return 1;
    else
      return 0;
  }
  int res = 0;
  res += (long long)solve(first - 1, st, ed) *
         power(2, mlen[first - 2], 1000000007) % 1000000007;
  res += (long long)solve(first - 2, st, ed) *
         power(2, mlen[first - 1], 1000000007) % 1000000007;
  res %= 1000000007;
  for (int i = st + 1; i < ed; i++) {
    res += (long long)calc(first - 1, 1, st, i) * calc(first - 2, 0, i, ed) %
           1000000007;
    res %= 1000000007;
  }
  flag[first][st][ed] = 1;
  return ans[first][st][ed] = res;
}
int main() {
  int n, first;
  cin >> n >> first;
  scanf("%s", s);
  len[0] = len[1] = mlen[0] = mlen[1] = 1;
  for (int i = 2; i < 111; i++) {
    mlen[i] = (mlen[i - 1] + mlen[i - 2]) % (1000000007 - 1);
    len[i] = len[i - 1] + len[i - 2];
    smin(len[i], 0x3f3f3f3f);
  }
  cout << solve(first, 0, n) << endl;
  return 0;
}