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;
using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
  if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
  if (t < u) t = u;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  os << "{";
  for (int i = 0; i < (v.size()); i++) {
    if (i) os << ",";
    os << v[i];
  }
  os << "}";
  return os;
}
template <unsigned int MOD>
struct ModInt {
  using uint = unsigned int;
  using ull = unsigned long long;
  using M = ModInt;
  uint v;
  ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
  M& set_norm(uint _v) {
    v = (_v < MOD) ? _v : _v - MOD;
    return *this;
  }
  explicit operator bool() const { return v != 0; }
  M operator+(const M& a) const { return M().set_norm(v + a.v); }
  M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
  M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
  M operator/(const M& a) const { return *this * a.inv(); }
  M& operator+=(const M& a) { return *this = *this + a; }
  M& operator-=(const M& a) { return *this = *this - a; }
  M& operator*=(const M& a) { return *this = *this * a; }
  M& operator/=(const M& a) { return *this = *this / a; }
  M operator-() const { return M() - *this; }
  M& operator++(int) { return *this = *this + 1; }
  M& operator--(int) { return *this = *this - 1; }
  M pow(ll n) const {
    if (n < 0) return inv().pow(-n);
    M x = *this, res = 1;
    while (n) {
      if (n & 1) res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }
  M inv() const {
    ll a = v, b = MOD, p = 1, q = 0, t;
    while (b != 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(p -= t * q, q);
    }
    return M(p);
  }
  bool operator==(const M& a) const { return v == a.v; }
  bool operator!=(const M& a) const { return v != a.v; }
  friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
  static int get_mod() { return MOD; }
};
using Mint = ModInt<1000000007>;
const Mint zero(0);
const Mint one(1);
bool iszero(Mint x) { return x.v == 0; }
bool isone(Mint x) { return x.v == 1; }
template <class T>
struct Matrix {
  int H, W;
  VV<T> a;
  Matrix() : H(0), W(0) {}
  Matrix(int H, int W) : H(H), W(W), a(VV<T>(H, V<T>(W))) {}
  Matrix(const VV<T>& v) : H(v.size()), W(v[0].size()), a(v) {}
  static Matrix E(int n) {
    Matrix a(n, n);
    for (int i = 0; i < (n); i++) a.set(i, i, 1);
    return a;
  }
  T at(int i, int j) const { return a[i][j]; }
  void set(int i, int j, T v) { a[i][j] = v; }
  Matrix operator+(const Matrix& r) const {
    assert(H == r.H && W == r.W);
    VV<T> v(H, V<T>(W));
    for (int i = 0; i < (H); i++)
      for (int j = 0; j < (W); j++) v[i][j] = a[i][j] + r.a[i][j];
    return Matrix(v);
  }
  Matrix operator-(const Matrix& r) const {
    assert(H == r.H && W == r.W);
    VV<T> v(H, V<T>(W));
    for (int i = 0; i < (H); i++)
      for (int j = 0; j < (W); j++) v[i][j] = a[i][j] - r.a[i][j];
    return Matrix(v);
  }
  Matrix operator*(const Matrix& r) const {
    assert(W == r.H);
    VV<T> v(H, V<T>(r.W));
    for (int i = 0; i < (H); i++)
      for (int k = 0; k < (W); k++)
        for (int j = 0; j < (r.W); j++) v[i][j] += a[i][k] * r.a[k][j];
    return Matrix(v);
  }
  Matrix& operator+=(const Matrix& r) { return (*this) = (*this) + r; }
  Matrix& operator-=(const Matrix& r) { return (*this) = (*this) - r; }
  Matrix& operator*=(const Matrix& r) { return (*this) = (*this) * r; }
  Matrix pow(ll n) const {
    assert(H == W);
    int h = H;
    Matrix x = *this, res(h, h);
    res = E(h);
    while (n > 0) {
      if (n & 1) res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }
  friend ostream& operator<<(ostream& o, const Matrix& A) {
    for (int i = 0; i < (A.H); i++) {
      for (int j = 0; j < (A.W); j++) o << A.a[i][j] << " ";
      o << endl;
    }
    return o;
  }
};
vector<int> pre_kmp(string pat) {
  int k;
  vector<int> table((int)pat.size() + 1);
  table[0] = -1;
  for (int i = 1; i <= pat.size(); ++i) {
    k = table[i - 1];
    while (k >= 0) {
      if (pat[k] == pat[i - 1])
        break;
      else
        k = table[k];
    }
    table[i] = k + 1;
  }
  return table;
}
using Mat = Matrix<Mint>;
int nxt[110][2];
V<int> pf;
string s;
int n;
Mat proc(int c) {
  Mat A(n + 2, n + 2);
  int ap = n + 1;
  A.set(ap, ap, 2);
  for (int i = 0; i <= n; ++i) {
    A.a[i][i]++;
    int nx = i;
    if (i == n) {
      nx = pf[nx];
    }
    while (nx >= 0 && s[nx] != '0' + c) {
      nx = pf[nx];
    }
    nx++;
    if (nx == n) {
      A.a[i][ap]++;
      nx = pf[nx];
    }
    A.a[i][nx]++;
  }
  return A;
}
int main() {
  int x;
  cin >> n >> x;
  cin >> s;
  pf = pre_kmp(s);
  (void(0));
  Mat a = proc(0), b = proc(1);
  for (int i = 2; i <= x; ++i) {
    auto c = b * a;
    a = b;
    b = c;
  }
  if (x == 0) {
    b = a;
  }
  Mat res(1, n + 2);
  res.set(0, 0, 1);
  res = res * b;
  cout << res.at(0, n + 1) << endl;
  return 0;
}