#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1000100;
const int P = 918357;
const int MOD1 = 1e9 + 7, MOD2 = 1e9 + 9;
int N, M;
int n0, n1;
string s;
string t;
long long hval1[MAXN], hval2[MAXN];
long long cpow1[MAXN], cpow2[MAXN];
long long ghash(int cloc, int len) {
  long long h1 =
      ((hval1[cloc + len] - cpow1[len] * hval1[cloc]) % MOD1 + MOD1) % MOD1;
  long long h2 =
      ((hval2[cloc + len] - cpow2[len] * hval2[cloc]) % MOD2 + MOD2) % MOD2;
  return h1 * MOD2 + h2;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cpow1[0] = cpow2[0] = 1;
  for (int i = 1; i < MAXN; i++) {
    cpow1[i] = (cpow1[i - 1] * P) % MOD1;
    cpow2[i] = (cpow2[i - 1] * P) % MOD2;
  }
  cin >> s >> t;
  N = s.length();
  M = t.length();
  hval1[0] = hval2[0] = 0;
  for (int i = 0; i < M; i++) {
    hval1[i + 1] = (hval1[i] * P + t[i]) % MOD1;
    hval2[i + 1] = (hval2[i] * P + t[i]) % MOD2;
  }
  n0 = n1 = 0;
  for (int i = 0; i < N; i++) {
    if (s[i] == '0')
      n0++;
    else
      n1++;
  }
  int ans = 0;
  for (int nleft = 1; nleft * n0 <= M; nleft++) {
    int nright = (M - nleft * n0) / n1;
    if (nright >= 1 && nleft * n0 + nright * n1 == M) {
      long long h0 = -1, h1 = -1;
      bool bad = false;
      int cloc = 0;
      for (int i = 0; i < N; i++) {
        if (s[i] == '0') {
          long long hnew = ghash(cloc, nleft);
          if (h0 == -1)
            h0 = hnew;
          else if (h0 != hnew)
            bad = true;
          cloc += nleft;
        } else {
          long long hnew = ghash(cloc, nright);
          if (h1 == -1)
            h1 = hnew;
          else if (h1 != hnew)
            bad = true;
          cloc += nright;
        }
      }
      if (nleft == nright && h0 == h1) bad = true;
      if (!bad) {
        ans++;
      }
    }
  }
  cout << ans << "\n";
}

### 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;
const int MAXN = 1000100;
const int P = 918357;
const int MOD1 = 1e9 + 7, MOD2 = 1e9 + 9;
int N, M;
int n0, n1;
string s;
string t;
long long hval1[MAXN], hval2[MAXN];
long long cpow1[MAXN], cpow2[MAXN];
long long ghash(int cloc, int len) {
  long long h1 =
      ((hval1[cloc + len] - cpow1[len] * hval1[cloc]) % MOD1 + MOD1) % MOD1;
  long long h2 =
      ((hval2[cloc + len] - cpow2[len] * hval2[cloc]) % MOD2 + MOD2) % MOD2;
  return h1 * MOD2 + h2;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cpow1[0] = cpow2[0] = 1;
  for (int i = 1; i < MAXN; i++) {
    cpow1[i] = (cpow1[i - 1] * P) % MOD1;
    cpow2[i] = (cpow2[i - 1] * P) % MOD2;
  }
  cin >> s >> t;
  N = s.length();
  M = t.length();
  hval1[0] = hval2[0] = 0;
  for (int i = 0; i < M; i++) {
    hval1[i + 1] = (hval1[i] * P + t[i]) % MOD1;
    hval2[i + 1] = (hval2[i] * P + t[i]) % MOD2;
  }
  n0 = n1 = 0;
  for (int i = 0; i < N; i++) {
    if (s[i] == '0')
      n0++;
    else
      n1++;
  }
  int ans = 0;
  for (int nleft = 1; nleft * n0 <= M; nleft++) {
    int nright = (M - nleft * n0) / n1;
    if (nright >= 1 && nleft * n0 + nright * n1 == M) {
      long long h0 = -1, h1 = -1;
      bool bad = false;
      int cloc = 0;
      for (int i = 0; i < N; i++) {
        if (s[i] == '0') {
          long long hnew = ghash(cloc, nleft);
          if (h0 == -1)
            h0 = hnew;
          else if (h0 != hnew)
            bad = true;
          cloc += nleft;
        } else {
          long long hnew = ghash(cloc, nright);
          if (h1 == -1)
            h1 = hnew;
          else if (h1 != hnew)
            bad = true;
          cloc += nright;
        }
      }
      if (nleft == nright && h0 == h1) bad = true;
      if (!bad) {
        ans++;
      }
    }
  }
  cout << ans << "\n";
}

```