#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
using namespace std;
void itval(istream_iterator<string> it) {}
template <typename T, typename... Args>
void itval(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  itval(++it, args...);
}
const long long int MOD = 1e9 + 7;
template <typename T>
inline void print(T x) {
  cout << x << "\n";
}
template <typename T>
inline void printvec(T x) {
  for (auto a : x) cout << a << ' ';
  cout << '\n';
}
struct custom {
  bool operator()(const pair<int, pair<int, int> > &p1,
                  const pair<int, pair<int, int> > &p2) const {
    return p1.first < p2.first;
  }
};
long long int get_pow(long long int a, long long int b, long long int M = MOD) {
  long long int res = 1;
  while (b) {
    if (b & 1) res = (res * a) % M;
    a = (a * a) % M;
    b >>= 1;
  }
  return res;
}
const long long int N = 1e2 + 5, inf = 2e18;
void solve() {
  string s, t;
  cin >> s >> t;
  int n = s.length(), m = t.length();
  if (m > n) {
    cout << "No\n";
    return;
  }
  std::vector<long long int> pos[26], post[26];
  for (long long int i = (long long int)0; i < (long long int)(n); i++) {
    pos[s[i] - 'a'].push_back(i);
  }
  for (long long int i = (long long int)0; i < (long long int)(m); i++) {
    post[t[i] - 'a'].push_back(i);
  }
  vector<long long> pref(n, 0), suf(n, 0);
  vector<bool> up(n, false), down(n, false);
  int c = 0, cnt = 0;
  for (long long int i = (long long int)0; i < (long long int)(n); i++) {
    if (c < m && s[i] == t[c]) {
      ++cnt;
      c++;
      up[i] = 1;
    }
    pref[i] = cnt;
  }
  if (c != m) {
    cout << "No\n";
    return;
  }
  c = m - 1;
  cnt = 0;
  for (int j = n - 1; j >= 0; j--) {
    if (c >= 0 && s[j] == t[c]) {
      ++cnt;
      c--;
      down[j] = 1;
    }
    suf[j] = cnt;
  }
  for (long long int i = (long long int)0; i < (long long int)(n); i++) {
    if (up[i] || down[i]) continue;
    if (pref[i] + suf[i] < m) {
      cout << "No\n";
      return;
    }
    if (post[s[i] - 'a'].empty()) {
      cout << "No\n";
      return;
    }
    int d = m - suf[i] - 1;
    auto it = lower_bound(post[s[i] - 'a'].begin(), post[s[i] - 'a'].end(), d);
    if (it == post[s[i] - 'a'].end()) {
      cout << "No\n";
      return;
    }
    if (*it > pref[i]) {
      cout << "No\n";
      return;
    }
  }
  cout << "Yes\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int test = 1;
  clock_t z = clock();
  for (long long int tes = (long long int)0; tes < (long long int)(test);
       tes++) {
    solve();
  }
  fprintf(stderr, "Total Time:%.4f\n", (double)(clock() - z) / CLOCKS_PER_SEC),
      fflush(stderr);
  return 0;
}
