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;
#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
const long long N = 1e6 + 9, mod = 1e9 + 7;
template <int32_t MOD>
struct modint {
  int32_t value;
  modint() = default;
  modint(int32_t value_) : value(value_) {}
  inline modint<MOD> operator+(modint<MOD> other) const {
    int32_t c = this->value + other.value;
    return modint<MOD>(c >= MOD ? c - MOD : c);
  }
  inline modint<MOD> operator-(modint<MOD> other) const {
    int32_t c = this->value - other.value;
    return modint<MOD>(c < 0 ? c + MOD : c);
  }
  inline modint<MOD> operator*(modint<MOD> other) const {
    int32_t c = (int64_t)this->value * other.value % MOD;
    return modint<MOD>(c < 0 ? c + MOD : c);
  }
  inline modint<MOD> &operator+=(modint<MOD> other) {
    this->value += other.value;
    if (this->value >= MOD) this->value -= MOD;
    return *this;
  }
  inline modint<MOD> &operator-=(modint<MOD> other) {
    this->value -= other.value;
    if (this->value < 0) this->value += MOD;
    return *this;
  }
  inline modint<MOD> &operator*=(modint<MOD> other) {
    this->value = (int64_t)this->value * other.value % MOD;
    if (this->value < 0) this->value += MOD;
    return *this;
  }
  inline modint<MOD> operator-() const {
    return modint<MOD>(this->value ? MOD - this->value : 0);
  }
  modint<MOD> pow(uint64_t k) const {
    modint<MOD> x = *this, y = 1;
    for (; k; k >>= 1) {
      if (k & 1) y *= x;
      x *= x;
    }
    return y;
  }
  modint<MOD> inv() const { return pow(MOD - 2); }
  inline modint<MOD> operator/(modint<MOD> other) const {
    return *this * other.inv();
  }
  inline modint<MOD> operator/=(modint<MOD> other) {
    return *this *= other.inv();
  }
  inline bool operator==(modint<MOD> other) const {
    return value == other.value;
  }
  inline bool operator!=(modint<MOD> other) const {
    return value != other.value;
  }
  inline bool operator<(modint<MOD> other) const { return value < other.value; }
  inline bool operator>(modint<MOD> other) const { return value > other.value; }
};
template <int32_t MOD>
modint<MOD> operator*(int64_t value, modint<MOD> n) {
  return modint<MOD>(value) * n;
}
template <int32_t MOD>
modint<MOD> operator*(int32_t value, modint<MOD> n) {
  return modint<MOD>(value % MOD) * n;
}
template <int32_t MOD>
istream &operator>>(istream &in, modint<MOD> &n) {
  return in >> n.value;
}
template <int32_t MOD>
ostream &operator<<(ostream &out, modint<MOD> n) {
  return out << n.value;
}
using mint = modint<mod>;
vector<mint> BerlekampMassey(vector<mint> S) {
  long long n = (long long)S.size(), L = 0, m = 0;
  vector<mint> C(n), B(n), T;
  C[0] = B[0] = 1;
  mint b = 1;
  for (long long i = 0; i < n; i++) {
    ++m;
    mint d = S[i];
    for (long long j = 1; j <= L; j++) d += C[j] * S[i - j];
    if (d == 0) continue;
    T = C;
    mint coef = d * b.inv();
    for (long long j = m; j < n; j++) C[j] -= coef * B[j - m];
    if (2 * L > i) continue;
    L = i + 1 - L;
    B = T;
    b = d;
    m = 0;
  }
  C.resize(L + 1);
  C.erase(C.begin());
  for (auto &x : C) x *= -1;
  return C;
}
vector<mint> combine(long long n, vector<mint> &a, vector<mint> &b,
                     vector<mint> &tr) {
  vector<mint> res(n * 2 + 1, 0);
  for (long long i = 0; i < n + 1; i++) {
    for (long long j = 0; j < n + 1; j++) res[i + j] += a[i] * b[j];
  }
  for (long long i = 2 * n; i > n; --i) {
    for (long long j = 0; j < n; j++) res[i - 1 - j] += res[i] * tr[j];
  }
  res.resize(n + 1);
  return res;
};
mint LinearRecurrence(vector<mint> &S, vector<mint> &tr, long long k) {
  long long n = S.size();
  assert(n == (long long)tr.size());
  if (k < 0LL) return mint(0);
  if (n == 0) return 0;
  if (k < n) return S[k];
  vector<mint> pol(n + 1), e(pol);
  pol[0] = e[1] = 1;
  for (++k; k; k /= 2) {
    if (k % 2) pol = combine(n, pol, e, tr);
    e = combine(n, e, e, tr);
  }
  mint res = 0;
  for (long long i = 0; i < n; i++) res += pol[i + 1] * S[i];
  return res;
}
mint z_match(string s, long long x) {
  long long n = (long long)s.length();
  vector<long long> z(n);
  long long ans = 0;
  for (long long i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r)
      z[i] = min(r - i + 1, z[i - l]);
    else
      z[i] = 0;
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) ++z[i];
    if (i + z[i] - 1 > r) l = i, r = i + z[i] - 1;
    if (z[i] == x) ans++;
  }
  return mint(ans);
}
vector<mint> prea, preb, preab, preba, prebb;
void solve() {
  vector<string> v;
  v.push_back("a");
  v.push_back("b");
  vector<mint> sha, shb, shab, shba, shbb;
  for (long long i = 1; i <= 8; i++) {
    v.push_back(v[i] + v[i - 1]);
    sha.push_back(z_match("a#" + v.back(), 1));
    shb.push_back(z_match("b#" + v.back(), 1));
    shab.push_back(z_match("ab#" + v.back(), 2));
    shba.push_back(z_match("ba#" + v.back(), 2));
    shbb.push_back(z_match("bb#" + v.back(), 2));
  }
  for (long long i = 9; v.back().size() < 200000; i++) {
    v.push_back(v[i] + v[i - 1]);
  }
  long long k, m;
  cin >> k >> m;
  auto tra = BerlekampMassey(sha);
  auto trb = BerlekampMassey(shb);
  auto trab = BerlekampMassey(shab);
  auto trba = BerlekampMassey(shba);
  auto trbb = BerlekampMassey(shbb);
  sha.resize(tra.size());
  shb.resize(trb.size());
  shab.resize(trab.size());
  shba.resize(trba.size());
  shbb.resize(trbb.size());
  for (long long i = 0; i < v.size(); i++) {
    if (k - i - 3 < 0) break;
    prea.push_back(LinearRecurrence(sha, tra, k - i - 3));
    preb.push_back(LinearRecurrence(shb, trb, k - i - 3));
    preab.push_back(LinearRecurrence(shab, trab, k - i - 3));
    preba.push_back(LinearRecurrence(shba, trba, k - i - 3));
    prebb.push_back(LinearRecurrence(shbb, trbb, k - i - 3));
  }
  for (long long j = 0; j < m; j++) {
    string s;
    cin >> s;
    {
      long long idx = 0;
      for (long long i = 0; i < v.size(); i++)
        if (v[i].size() >= s.size()) {
          idx = i;
          break;
        }
      if (k <= idx + 3) {
        cout << z_match(s + "#" + v[k - 1], s.size()) << '\n';
        continue;
      }
      mint a = z_match(s + "#" + v[idx], (long long)s.size());
      mint b = z_match(s + "#" + v[idx + 1], s.size());
      mint ab = z_match(s + "#" + v[idx] + v[idx + 1], s.size()) - a - b;
      mint ba = z_match(s + "#" + v[idx + 1] + v[idx], s.size()) - a - b;
      mint bb = z_match(s + "#" + v[idx + 1] + v[idx + 1], s.size()) - b - b;
      mint ans(0);
      ans += prea[idx] * a;
      ans += preb[idx] * b;
      ans += preab[idx] * ab;
      ans += preba[idx] * ba;
      ans += prebb[idx] * bb;
      cout << ans << '\n';
    }
  }
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long t = 1;
  while (t--) solve();
}