Problem: Fibonacci strings are defined as follows: 

  * f1 = «a» 
  * f2 = «b» 
  * fn = fn - 1 fn - 2, n > 2



Thus, the first five Fibonacci strings are: "a", "b", "ba", "bab", "babba".

You are given a Fibonacci string and m strings si. For each string si, find the number of times it occurs in the given Fibonacci string as a substring.

Input

The first line contains two space-separated integers k and m — the number of a Fibonacci string and the number of queries, correspondingly.

Next m lines contain strings si that correspond to the queries. It is guaranteed that strings si aren't empty and consist only of characters "a" and "b".

The input limitations for getting 30 points are: 

  * 1 ≤ k ≤ 3000
  * 1 ≤ m ≤ 3000
  * The total length of strings si doesn't exceed 3000



The input limitations for getting 100 points are: 

  * 1 ≤ k ≤ 1018
  * 1 ≤ m ≤ 104
  * The total length of strings si doesn't exceed 105



Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Output

For each string si print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo 1000000007 (109 + 7). Print the answers for the strings in the order in which they are given in the input.

Examples

Input

6 5
a
b
ab
ba
aba


Output

3
5
3
3
1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double EPS = -1e8;
const double Pi = acos(-1);
bool inline equ(double a, double b) { return fabs(a - b) < EPS; }
const int MAXN = 200010;
const long long MOD = 1000000007ll;
inline long long add(long long a, long long b) { return (a + b) % MOD; }
inline long long mul(long long a, long long b) { return (a * b) % MOD; }
inline long long sub(long long a, long long b) { return (a - b + MOD) % MOD; }
struct Mat {
  long long dat[4][4];
  long long* operator[](int i) { return dat[i]; }
};
Mat I{{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}};
Mat F{{{1, 1, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}};
Mat operator*(Mat A, Mat B) {
  Mat C;
  for (int i = (0); i <= (3); i++)
    for (int j = (0); j <= (3); j++) {
      C[i][j] = 0;
      for (int k = (0); k <= (3); k++) C[i][j] += mul(A[i][k], B[k][j]);
      C[i][j] %= MOD;
    }
  return C;
}
Mat pw(Mat A, long long x) {
  assert(x >= 0);
  Mat base = A, ret = I;
  while (x > 0) {
    if (x & 1) ret = base * ret;
    base = base * base;
    x >>= 1;
  }
  return ret;
}
long long K;
int m;
inline int cnt(const string& t, const string& p) {
  static int f[MAXN];
  if ((int)(p).size() > (int)(t).size()) return 0;
  for (int i = 1, j = f[0] = -1; i < (int)(p).size(); i++) {
    while (j >= 0 && p[j + 1] != p[i]) j = f[j];
    if (p[j + 1] == p[i]) j++;
    f[i] = j;
  }
  int res = 0;
  for (int i = 0, j = -1; i < (int)(t).size(); i++) {
    while (j >= 0 && p[j + 1] != t[i]) j = f[j];
    if (p[j + 1] == t[i]) j++;
    if (j == (int)(p).size() - 1) {
      res++;
      j = f[j];
    }
  }
  return res;
}
string fib[33];
inline long long solve(const string& s) {
  if (K == 1) return s == "a";
  if (K == 2) return s == "b";
  string A = "a", B = "b";
  int i;
  for (i = 3; i <= K; i++) {
    assert(i < 30);
    if ((int)(fib[i - 1]).size() >= (int)(s).size() || i == K) {
      B = fib[i];
      A = fib[i - 1];
      break;
    }
  }
  string fip1 = fib[i + 1];
  long long CA = cnt(A, s);
  long long CB = cnt(B, s);
  long long CAB = cnt(A + B, s) - CA - CB;
  long long CBB = cnt(B + B, s) - CB - CB;
  long long Sip1 = cnt(fip1, s);
  if (K == i) return CB;
  if (K == i + 1) return Sip1;
  Mat Ans = pw(F, K - (long long)(i + 1));
  return add(add(mul(Ans[0][0], Sip1), mul(Ans[0][1], CB)),
             add(mul(Ans[0][2], CAB), mul(Ans[0][3], CBB)));
}
int main() {
  fib[1] = "a";
  fib[2] = "b";
  for (int i = (3); i <= (30); i++) fib[i] = fib[i - 1] + fib[i - 2];
  ios_base::sync_with_stdio(0);
  cin >> K >> m;
  for (int i = (1); i <= (m); i++) {
    string str;
    cin >> str;
    cout << solve(str) << '\n';
  }
}