Problem: If you have gone that far, you'll probably skip unnecessary legends anyway...

You are given a binary string <image> and an integer <image>. Find the number of integers k, 0 ≤ k < N, such that for all i = 0, 1, ..., m - 1

<image> Print the answer modulo 109 + 7.

Input

In the first line of input there is a string s consisting of 0's and 1's (1 ≤ |s| ≤ 40).

In the next line of input there is an integer n (1 ≤ n ≤ 5·105).

Each of the next n lines contains two space-separated integers pi, αi (1 ≤ pi, αi ≤ 109, pi is prime). All pi are distinct.

Output

A single integer — the answer to the problem.

Examples

Input

1
2
2 1
3 1


Output

2


Input

01
2
3 2
5 1


Output

15


Input

1011
1
3 1000000000


Output

411979884

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const long double eps = 1e-10;
const int step[8][2] = {{-1, 0}, {0, 1}, {1, 0},  {0, -1},
                        {-1, 1}, {1, 1}, {1, -1}, {-1, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <typename t, typename t1>
t min1(t a, t1 b) {
  return a < b ? a : b;
}
template <typename t, typename... arg>
t min1(t a, arg... arr) {
  return min1(a, min1(arr...));
}
template <typename t, typename t1>
t max1(t a, t1 b) {
  return a > b ? a : b;
}
template <typename t, typename... arg>
t max1(t a, arg... arr) {
  return max1(a, max1(arr...));
}
inline int jud(double a, double b) {
  if (abs(a) < eps && abs(b) < eps)
    return 0;
  else if (abs1(a - b) / max(abs1(a), abs1(b)) < eps)
    return 0;
  if (a < b) return -1;
  return 1;
}
template <typename t>
inline int jud(t a, t b) {
  if (a < b) return -1;
  if (a == b) return 0;
  return 1;
}
template <typename it, typename t1>
inline int find(t1 val, it a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 0) return 0;
  int be = 0, en = na - 1;
  if (*a <= *(a + na - 1)) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(*(a + be), val) == 1) be--;
    if (!f_small && jud(*(a + be), val) == -1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(*(a + be), val) == -1) be--;
    if (f_small && jud(*(a + be), val) == 1) be++;
  }
  return be;
}
template <class T>
inline T lowb(T num) {
  return num & (-num);
}
inline int bitnum(unsigned int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(unsigned long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitnum(long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitmaxl(unsigned int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(unsigned long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
inline int bitmaxl(long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
long long pow(long long n, long long m, long long mod = 0) {
  if (m < 0) return 0;
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <class t1, class t2>
inline void add(t1 &a, t2 b, int mod = -1) {
  if (mod == -1) mod = 1000000007;
  a += b;
  while (a >= mod) a -= mod;
  while (a < 0) a += mod;
}
template <class t>
void output1(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) cerr << arr[i] << ' ';
  cerr << endl;
}
template <class t>
void output2(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) output1(arr[i]);
}
const int mod = 1000000007;
const int maxn = 501000;
char str[maxn];
int np;
vector<pair<long long, long long> > pri;
unordered_map<long long, long long> ump[2];
int main() {
  ios_base::sync_with_stdio(0);
  scanf("%s", str);
  int l = strlen(str);
  long long mask = 0;
  for (int i = 0; i < l; i++)
    if (str[i] == '0') mask |= 1ll << i;
  scanf("%d", &np);
  for (int i = 0; i < np; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    pri.push_back(make_pair(a, b));
  }
  sort(pri.begin(), pri.end());
  ump[0][0] = 1;
  int now = 0, nxt = 1;
  for (auto it : pri) {
    ump[nxt].clear();
    if (it.first >= l) continue;
    long long rmask = 1ll << l, mask1 = 0;
    rmask--;
    for (int i = 0; i < l; i += it.first) mask1 |= 1ll << i;
    for (int i = 0; i < it.first; i++) {
      long long tmask = rmask & (mask1 << i);
      if ((tmask & mask) != tmask) continue;
      for (auto rit : ump[now]) {
        long long rt = rit.first | tmask;
        auto tit = ump[nxt].find(rt);
        if (tit == ump[nxt].end())
          tit = ump[nxt].insert(make_pair(rt, 0)).first;
        assert(tit->first == rt);
        add(tit->second, rit.second);
      }
    }
    swap(now, nxt);
  }
  long long dp[44];
  memset(dp, 0, sizeof(dp));
  for (auto it : ump[now]) {
    assert((it.first & mask) == it.first);
    add(dp[bitnum(mask ^ it.first)], it.second);
  }
  long long mul = 1;
  int delta = l - bitnum(mask);
  for (auto it : pri) {
    if (it.first >= l) {
      for (int i = 0; i <= l; i++)
        if (dp[i]) {
          if (i) add(dp[i - 1], dp[i] * i % mod);
          dp[i] *= 1ll * (it.first - i - delta);
          dp[i] %= mod;
        }
    }
    mul = mul * pow(it.first, it.second - 1, mod) % mod;
  }
  cout << mul * dp[0] % mod << endl;
  return 0;
}