#include <bits/stdc++.h>
using namespace std;
struct RollingHash {
  vector<int64_t> hash;
  vector<int64_t> base_pow;
  int64_t base, mod;
  const int64_t DEFAULT_BASE = 1009, DEFAULT_MOD = 1e9 + 7;
  RollingHash(string S = "", int64_t base_ = -1, int64_t mod_ = -1) {
    base = base_ > 0 ? base_ : DEFAULT_BASE;
    mod = mod_ > 0 ? mod_ : DEFAULT_MOD;
    if (S.size() > 0) initialize(S);
  }
  void initialize(string S) {
    hash.resize(S.size() + 1);
    base_pow.resize(S.size() + 1);
    hash[0] = 0;
    base_pow[0] = 1;
    for (int i = 1; i <= S.size(); i++) {
      hash[i] = (hash[i - 1] * base + S[i - 1]) % mod;
      base_pow[i] = base_pow[i - 1] * base % mod;
    }
  }
  int64_t between(int a, int b) {
    return (mod + hash[b] - hash[a] * base_pow[b - a] % mod) % mod;
  }
};
int main() {
  string S, T;
  cin >> S >> T;
  int num[2] = {0, 0};
  vector<int> prv[2][2];
  for (int i = 0; i < S.size(); i++) {
    int b = (S[i] == '1');
    prv[b][0].push_back(num[0]);
    prv[b][1].push_back(num[1]);
    num[b]++;
  }
  RollingHash rh(T);
  int64_t hashT = rh.between(0, T.size());
  int ans = 0;
  for (int len0 = 1; len0 * num[0] < T.size(); len0++) {
    int r = T.size() - len0 * num[0];
    if (r % num[1] != 0) continue;
    int len1 = r / num[1];
    int64_t hash[2];
    hash[0] = rh.between(len1 * prv[0][1][0], len1 * prv[0][1][0] + len0);
    hash[1] = rh.between(len0 * prv[1][0][0], len0 * prv[1][0][0] + len1);
    if (len0 == len1 && hash[0] == hash[1]) continue;
    int64_t sum = 0;
    int len[2] = {len0, len1};
    for (int k = 0; k < 2; k++) {
      for (int i = 0; i < prv[k][0].size(); i++) {
        int prv_sum = prv[k][0][i] * len0 + prv[k][1][i] * len1;
        sum += hash[k] * rh.base_pow[T.size() - prv_sum - len[k]] % rh.mod;
        sum %= rh.mod;
      }
    }
    if (sum == hashT) ans++;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

One of Arkady's friends works at a huge radio telescope. A few decades ago the telescope has sent a signal s towards a faraway galaxy. Recently they've received a response t which they believe to be a response from aliens! The scientists now want to check if the signal t is similar to s.

The original signal s was a sequence of zeros and ones (everyone knows that binary code is the universe-wide language). The returned signal t, however, does not look as easy as s, but the scientists don't give up! They represented t as a sequence of English letters and say that t is similar to s if you can replace all zeros in s with some string r_0 and all ones in s with some other string r_1 and obtain t. The strings r_0 and r_1 must be different and non-empty.

Please help Arkady's friend and find the number of possible replacements for zeros and ones (the number of pairs of strings r_0 and r_1) that transform s to t.

Input

The first line contains a string s (2 ≤ |s| ≤ 10^5) consisting of zeros and ones — the original signal.

The second line contains a string t (1 ≤ |t| ≤ 10^6) consisting of lowercase English letters only — the received signal.

It is guaranteed, that the string s contains at least one '0' and at least one '1'.

Output

Print a single integer — the number of pairs of strings r_0 and r_1 that transform s to t.

In case there are no such pairs, print 0.

Examples

Input


01
aaaaaa


Output


4


Input


001
kokokokotlin


Output


2

Note

In the first example, the possible pairs (r_0, r_1) are as follows:

  * "a", "aaaaa" 
  * "aa", "aaaa" 
  * "aaaa", "aa" 
  * "aaaaa", "a" 



The pair "aaa", "aaa" is not allowed, since r_0 and r_1 must be different.

In the second example, the following pairs are possible: 

  * "ko", "kokotlin" 
  * "koko", "tlin" 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct RollingHash {
  vector<int64_t> hash;
  vector<int64_t> base_pow;
  int64_t base, mod;
  const int64_t DEFAULT_BASE = 1009, DEFAULT_MOD = 1e9 + 7;
  RollingHash(string S = "", int64_t base_ = -1, int64_t mod_ = -1) {
    base = base_ > 0 ? base_ : DEFAULT_BASE;
    mod = mod_ > 0 ? mod_ : DEFAULT_MOD;
    if (S.size() > 0) initialize(S);
  }
  void initialize(string S) {
    hash.resize(S.size() + 1);
    base_pow.resize(S.size() + 1);
    hash[0] = 0;
    base_pow[0] = 1;
    for (int i = 1; i <= S.size(); i++) {
      hash[i] = (hash[i - 1] * base + S[i - 1]) % mod;
      base_pow[i] = base_pow[i - 1] * base % mod;
    }
  }
  int64_t between(int a, int b) {
    return (mod + hash[b] - hash[a] * base_pow[b - a] % mod) % mod;
  }
};
int main() {
  string S, T;
  cin >> S >> T;
  int num[2] = {0, 0};
  vector<int> prv[2][2];
  for (int i = 0; i < S.size(); i++) {
    int b = (S[i] == '1');
    prv[b][0].push_back(num[0]);
    prv[b][1].push_back(num[1]);
    num[b]++;
  }
  RollingHash rh(T);
  int64_t hashT = rh.between(0, T.size());
  int ans = 0;
  for (int len0 = 1; len0 * num[0] < T.size(); len0++) {
    int r = T.size() - len0 * num[0];
    if (r % num[1] != 0) continue;
    int len1 = r / num[1];
    int64_t hash[2];
    hash[0] = rh.between(len1 * prv[0][1][0], len1 * prv[0][1][0] + len0);
    hash[1] = rh.between(len0 * prv[1][0][0], len0 * prv[1][0][0] + len1);
    if (len0 == len1 && hash[0] == hash[1]) continue;
    int64_t sum = 0;
    int len[2] = {len0, len1};
    for (int k = 0; k < 2; k++) {
      for (int i = 0; i < prv[k][0].size(); i++) {
        int prv_sum = prv[k][0][i] * len0 + prv[k][1][i] * len1;
        sum += hash[k] * rh.base_pow[T.size() - prv_sum - len[k]] % rh.mod;
        sum %= rh.mod;
      }
    }
    if (sum == hashT) ans++;
  }
  cout << ans << endl;
  return 0;
}

```