#include <bits/stdc++.h>
using namespace std;
inline int ri() {
  register int x = 0;
  register bool f = 0;
  register char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = 1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f ? -x : x;
}
void wi(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) wi(x / 10);
  putchar('0' + x % 10);
}
const int N = 1e6 + 7, p = 1e9 + 25, d = 31;
char s1[N], s2[N];
long long hs[N], expd[N];
inline long long geths(int l, int r) {
  return ((hs[r] - hs[l - 1] * expd[r - l + 1] % p) % p + p) % p;
}
int main() {
  int l1, l2, i, j, c0 = 0, c1 = 0, ans = 0, now, f1 = 0, lf1 = 0, flag;
  scanf("%s%s", s1 + 1, s2 + 1);
  l1 = strlen(s1 + 1), l2 = strlen(s2 + 1);
  for (i = 1; i <= l2; i++) hs[i] = (hs[i - 1] * d % p + s2[i] - 'a' + 1) % p;
  for (i = 1; i <= l1; i++) s1[i] -= '0';
  for (expd[0] = 1, i = 1; i <= l2 + 1; i++) expd[i] = expd[i - 1] * d % p;
  if (s1[1] == 1)
    for (i = 1; i <= l1; i++) s1[i] ^= 1;
  for (i = 1; i <= l1; i++) {
    if (s1[i] == 0)
      c0++;
    else
      c1++;
    if (!f1 && s1[i] == 1) {
      f1 = i;
      lf1 = 1;
      for (j = i + 1; s1[j] == 1; j++) lf1++;
    }
  }
  for (i = 1; i <= l2; i++) {
    if (l2 <= c0 * i) break;
    if ((l2 - c0 * i) % c1 != 0) continue;
    long long h0 = geths(1, i),
              h1 = geths((f1 - 1) * i + 1, (f1 - 1) * i + (l2 - c0 * i) / c1);
    if (h0 == h1) continue;
    for (j = flag = now = 1; j <= l1; j++) {
      if (s1[j] == 0) {
        if (h0 != geths(now, now + i - 1)) {
          flag = 0;
          break;
        }
        now += i;
      } else {
        if (h1 != geths(now, now + (l2 - c0 * i) / c1 - 1)) {
          flag = 0;
          break;
        }
        now += (l2 - c0 * i) / c1;
      }
    }
    ans += flag;
  }
  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;
inline int ri() {
  register int x = 0;
  register bool f = 0;
  register char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = 1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f ? -x : x;
}
void wi(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) wi(x / 10);
  putchar('0' + x % 10);
}
const int N = 1e6 + 7, p = 1e9 + 25, d = 31;
char s1[N], s2[N];
long long hs[N], expd[N];
inline long long geths(int l, int r) {
  return ((hs[r] - hs[l - 1] * expd[r - l + 1] % p) % p + p) % p;
}
int main() {
  int l1, l2, i, j, c0 = 0, c1 = 0, ans = 0, now, f1 = 0, lf1 = 0, flag;
  scanf("%s%s", s1 + 1, s2 + 1);
  l1 = strlen(s1 + 1), l2 = strlen(s2 + 1);
  for (i = 1; i <= l2; i++) hs[i] = (hs[i - 1] * d % p + s2[i] - 'a' + 1) % p;
  for (i = 1; i <= l1; i++) s1[i] -= '0';
  for (expd[0] = 1, i = 1; i <= l2 + 1; i++) expd[i] = expd[i - 1] * d % p;
  if (s1[1] == 1)
    for (i = 1; i <= l1; i++) s1[i] ^= 1;
  for (i = 1; i <= l1; i++) {
    if (s1[i] == 0)
      c0++;
    else
      c1++;
    if (!f1 && s1[i] == 1) {
      f1 = i;
      lf1 = 1;
      for (j = i + 1; s1[j] == 1; j++) lf1++;
    }
  }
  for (i = 1; i <= l2; i++) {
    if (l2 <= c0 * i) break;
    if ((l2 - c0 * i) % c1 != 0) continue;
    long long h0 = geths(1, i),
              h1 = geths((f1 - 1) * i + 1, (f1 - 1) * i + (l2 - c0 * i) / c1);
    if (h0 == h1) continue;
    for (j = flag = now = 1; j <= l1; j++) {
      if (s1[j] == 0) {
        if (h0 != geths(now, now + i - 1)) {
          flag = 0;
          break;
        }
        now += i;
      } else {
        if (h1 != geths(now, now + (l2 - c0 * i) / c1 - 1)) {
          flag = 0;
          break;
        }
        now += (l2 - c0 * i) / c1;
      }
    }
    ans += flag;
  }
  cout << ans << endl;
  return 0;
}

```