#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 100000;
long long p[MAXN];
long long dp[MAXN];
long long prime = 47;
long long mod = 1e9 + 7;
string s, t;
long long cnt0 = 0;
long long cnt1 = 0;
long long tsz, ssz;
long long h[1000001];
long long deg[1000001];
void preHash() {
  long long nowdeg = 1;
  long long now = 0;
  deg[0] = 1;
  for (long long i = 0; i < tsz; i++) {
    now *= prime;
    now += (long long)t[i];
    now %= mod;
    h[i + 1] = now;
    nowdeg *= prime;
    nowdeg %= mod;
    deg[i + 1] = nowdeg;
  }
}
long long Hash(long long i, long long j) {
  long long now = 0;
  long long faster;
  if (j <= tsz) faster = (h[j] - ((h[i] * deg[j - i]) % mod) + mod) % mod;
  return faster;
}
bool Check(long long r0, long long r1) {
  long long now = 0;
  long long hash0, hash1;
  bool h1, h0;
  h1 = h0 = false;
  bool flag = true;
  for (long long i = 0; i < ssz; i++) {
    if (!h0 && s[i] == '0') {
      hash0 = Hash(now, now + r0);
      h0 = true;
      now += r0;
      continue;
    }
    if (!h1 && s[i] == '1') {
      hash1 = Hash(now, now + r1);
      h1 = true;
      now += r1;
      continue;
    }
    if (s[i] == '0') {
      if (hash0 != Hash(now, now + r0)) flag = false;
      now += r0;
    }
    if (s[i] == '1') {
      if (hash1 != Hash(now, now + r1)) flag = false;
      now += r1;
    }
  }
  if (hash1 == hash0) flag = false;
  return flag;
}
signed main() {
  ios_base ::sync_with_stdio(0);
  cin >> s;
  cin >> t;
  tsz = t.size();
  ssz = s.size();
  long long ans = 0;
  for (long long i = 0; i < s.size(); i++) {
    if (s[i] == '0')
      cnt0++;
    else
      cnt1++;
  }
  preHash();
  for (long long i = 1; i < tsz; i++) {
    if (tsz >= cnt0 * i)
      if (cnt1 == 0 || ((tsz - cnt0 * i) % cnt1 == 0 &&
                        ((cnt1 == 0) ^ ((tsz - cnt0 * i) != 0)))) {
        long long rrr = 0;
        if (cnt1 != 0) rrr = (tsz - cnt0 * i) / cnt1;
        if (i * cnt0 + rrr * cnt1 == tsz)
          if (Check(i, rrr)) ans++;
      }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please formulate a CPP solution to 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 long long MAXN = 100000;
long long p[MAXN];
long long dp[MAXN];
long long prime = 47;
long long mod = 1e9 + 7;
string s, t;
long long cnt0 = 0;
long long cnt1 = 0;
long long tsz, ssz;
long long h[1000001];
long long deg[1000001];
void preHash() {
  long long nowdeg = 1;
  long long now = 0;
  deg[0] = 1;
  for (long long i = 0; i < tsz; i++) {
    now *= prime;
    now += (long long)t[i];
    now %= mod;
    h[i + 1] = now;
    nowdeg *= prime;
    nowdeg %= mod;
    deg[i + 1] = nowdeg;
  }
}
long long Hash(long long i, long long j) {
  long long now = 0;
  long long faster;
  if (j <= tsz) faster = (h[j] - ((h[i] * deg[j - i]) % mod) + mod) % mod;
  return faster;
}
bool Check(long long r0, long long r1) {
  long long now = 0;
  long long hash0, hash1;
  bool h1, h0;
  h1 = h0 = false;
  bool flag = true;
  for (long long i = 0; i < ssz; i++) {
    if (!h0 && s[i] == '0') {
      hash0 = Hash(now, now + r0);
      h0 = true;
      now += r0;
      continue;
    }
    if (!h1 && s[i] == '1') {
      hash1 = Hash(now, now + r1);
      h1 = true;
      now += r1;
      continue;
    }
    if (s[i] == '0') {
      if (hash0 != Hash(now, now + r0)) flag = false;
      now += r0;
    }
    if (s[i] == '1') {
      if (hash1 != Hash(now, now + r1)) flag = false;
      now += r1;
    }
  }
  if (hash1 == hash0) flag = false;
  return flag;
}
signed main() {
  ios_base ::sync_with_stdio(0);
  cin >> s;
  cin >> t;
  tsz = t.size();
  ssz = s.size();
  long long ans = 0;
  for (long long i = 0; i < s.size(); i++) {
    if (s[i] == '0')
      cnt0++;
    else
      cnt1++;
  }
  preHash();
  for (long long i = 1; i < tsz; i++) {
    if (tsz >= cnt0 * i)
      if (cnt1 == 0 || ((tsz - cnt0 * i) % cnt1 == 0 &&
                        ((cnt1 == 0) ^ ((tsz - cnt0 * i) != 0)))) {
        long long rrr = 0;
        if (cnt1 != 0) rrr = (tsz - cnt0 * i) / cnt1;
        if (i * cnt0 + rrr * cnt1 == tsz)
          if (Check(i, rrr)) ans++;
      }
  }
  cout << ans << endl;
  return 0;
}

```