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>
const long long MaxN = 105;
const long long p = 1e9 + 7;
template <class t>
inline void read(t &s) {
  s = 0;
  register long long f = 1;
  register char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) s = (s << 3) + (s << 1) + (c ^ 48), c = getchar();
  s *= f;
  return;
}
template <class t, class... A>
inline void read(t &x, A &...a) {
  read(x);
  read(a...);
}
template <class t>
inline void write(t x) {
  if (x < 0) putchar('-'), x = -x;
  long long buf[21], top = 0;
  while (x) buf[++top] = x % 10, x /= 10;
  if (!top) buf[++top] = 0;
  while (top) putchar(buf[top--] ^ '0');
  return;
}
inline void setIn(std::string s) {
  freopen(s.c_str(), "r", stdin);
  return;
}
inline void setOut(std::string s) {
  freopen(s.c_str(), "w", stdout);
  return;
}
inline void setIO(std::string s = "") {
  setIn(s + ".in");
  setOut(s + ".out");
  return;
}
template <class t>
inline bool ckmin(t &x, t y) {
  if (x > y) {
    x = y;
    return 1;
  }
  return 0;
}
template <class t>
inline bool ckmax(t &x, t y) {
  if (x < y) {
    x = y;
    return 1;
  }
  return 0;
}
inline long long lowbit(long long x) { return x & (-x); }
long long kmp[MaxN], n, K;
char s[MaxN];
struct Vec {
  long long a[MaxN];
  Vec() { std::memset(a, 0, sizeof a); }
} ans;
struct Node {
  long long a[MaxN][MaxN];
  Node() { std::memset(a, 0, sizeof a); }
  inline Node operator*(const Node &nt) const {
    Node res;
    for (long long k = 0; k <= n; ++k)
      for (long long i = 0; i <= n; ++i)
        for (long long j = 0; j <= n; ++j)
          (res.a[i][j] += a[i][k] * nt.a[k][j]) %= p;
    return res;
  }
  inline Vec operator*(const Vec &nt) const {
    Vec res;
    for (long long k = 0; k <= n; ++k)
      for (long long i = 0; i <= n; ++i) (res.a[i] += a[i][k] * nt.a[k]) %= p;
    return res;
  }
} I, base, f[MaxN];
inline long long calc(long long x, char y) {
  while (x && s[x + 1] != y) x = kmp[x];
  return s[x + 1] == y ? x + 1 : 0;
}
signed main(void) {
  read(n, K);
  std::scanf("%s", s + 1);
  register long long pos = 0;
  for (long long i = 2; i <= n; ++i) {
    while (pos && s[pos + 1] != s[i]) pos = kmp[pos];
    if (s[pos + 1] == s[i]) ++pos;
    kmp[i] = pos;
  }
  for (long long i = 0; i < 2; ++i)
    for (long long j = 0; j < n; ++j) {
      register long long to = calc(j, i + '0');
      if (to == n) ++f[i].a[kmp[n]][j];
      ++f[i].a[to][j], ++f[i].a[j][j];
    }
  f[0].a[n][n] = f[1].a[n][n] = 2;
  ans.a[0] = 1;
  for (long long i = 2; i <= K; ++i) f[i] = f[i - 2] * f[i - 1];
  write((f[K] * ans).a[n]), std::puts("");
  return 0;
}