func_code_string: #include <bits/stdc++.h>   using namespace std;   long base;   vector<long> vec[2000];   long can[200][200];   long lcm[200];   long long n, k;   vector<vector<long> > mult(vector<vector<long> > a, vector<vector<long> > b) {     vector<vector<long> > v;     v.resize(a.size());     for (int i = 0; i < v.size(); i++) v[i].resize(a[0].size());     for (int i = 0; i < v.size(); i++)       for (int j = 0; j < v.size(); j++) v[i][j] = 0;     for (int k = 0; k < v.size(); k++)       for (int i = 0; i < v.size(); i++)         for (int j = 0; j < v.size(); j++)           v[i][j] += a[i][k] * b[k][j], v[i][j] %= base;     return v;   }   vector<vector<long> > one(long sz) {     vector<vector<long> > v;     v.resize(sz);     for (int i = 0; i < v.size(); i++) v[i].resize(sz);     for (int i = 0; i < v.size(); i++)       for (int j = 0; j < v.size(); j++) v[i][j] = (i == j);     return v;   }   vector<vector<long> > pw(vector<vector<long> > a, long long b) {     if (b == 0) return one(a.size());     if (b % 2) return mult(a, pw(a, b - 1));     return pw(mult(a, a), b / 2);   }   vector<long> decomp(long state) {     vector<long> res;     for (int i = 25; i >= 0; --i)       if (vec[i].size())         res.push_back(state % lcm[i]), state /= lcm[i];       else         res.push_back(1);     reverse(res.begin(), res.end());     return res;   }   long mov(long a, long b) {     vector<long> v1, v2;     v1 = decomp(a);     v2 = decomp(b);     long free = 0;     long found = 0;     for (int i = 0; i < 26; i++) {       if (vec[i].size() == 0) continue;       if ((v1[i] + 1) % lcm[i] == v2[i]) {         if (lcm[i] == 1)           free++;         else if (found == 0)           found = 1;         else           return 0;       } else if (v1[i] != v2[i])         return 0;     }     if (found) return 1;     return free;   }   string st;   long val;   long total;   long gcd(long a, long b) {     while (a && b) a > b ? a %= b : b %= a;     return a + b;   }   vector<vector<long> > res;   bool bad(long x, long ps) {     for (int i = 0; i < vec[ps].size(); i++)       if (x % vec[ps][i] == 0) return false;     return true;   }   bool check(vector<long> v) {     for (long i = 0; i < 26; i++) {       if (vec[i].size() == 0) continue;       if (bad(v[i], i)) return false;     }     return true;   }   void show(vector<vector<long> > v) {     for (int i = 0; i < v.size(); i++) {       for (int j = 0; j < v[i].size(); j++) cout << v[i][j] <<    ;       cout << endl;     }     cout << endl;   }   int main() {     ios_base::sync_with_stdio(0);     base = 12345;     cin >> n >> k;     for (int i = 1; i <= k; i++) {       cin >> st >> val;       vec[st[0] -  A ].push_back(val);       can[st[0] -  A ][val] = 1;     }     total = 1;     for (int i = 0; i < 26; i++)       if (vec[i].size()) {         lcm[i] = 1;         for (int j = 0; j < vec[i].size(); j++) {           long q = vec[i][j];           lcm[i] = lcm[i] * q / gcd(lcm[i], q);         }         total *= lcm[i];       }     res.resize(total);     for (int i = 0; i < res.size(); i++) res[i].resize(total);     for (int i = 0; i < total; i++)       for (int j = 0; j < total; j++) res[i][j] = mov(i, j);     res = pw(res, n);     long ans = 0;     for (int i = 0; i < total; i++) {       vector<long> v = decomp(i);       if (check(v)) ans += res[0][i], ans %= base;     }     cout << ans << endl;     cin.get();     cin.get();     return 0;   }   