A8746. Two Strings

A subsequence of length $|x|$ of string $s=s_{1}s_{2}...\ s_{|s|}$ (where $|s|$ is the length of string $s$ ) is a string $x=s_{k1}s_{k2}...\ s_{k|x|}$ $(1<=k_{1}<k_{2}<...<k_{|x|}<=|s|)$ .

You've got two strings — $s$ and $t$ . Let's consider all subsequences of string $s$ , coinciding with string $t$ . Is it true that each character of string $s$ occurs in at least one of these subsequences? In other words, is it true that for all $i$ $(1<=i<=|s|)$ , there is such subsequence $x=s_{k1}s_{k2}...\ s_{k|x|}$ of string $s$ , that $x=t$ and for some $j$ $(1<=j<=|x|)$ $k_{j}=i$ .

The first line contains string $s$ , the second line contains string $t$ . Each line consists only of lowercase English letters. The given strings are non-empty, the length of each string does not exceed $2·10^{5}$ .

Print "Yes" (without the quotes), if each character of the string $s$ occurs in at least one of the described subsequences, or "No" (without the quotes) otherwise.

In the first sample string $t$ can occur in the string $s$ as a subsequence in three ways: abab, abab and abab. In these occurrences each character of string $s$ occurs at least once.

In the second sample the 4-th character of the string $s$ doesn't occur in any occurrence of string $t$ .

In the third sample there is no occurrence of string $t$ in string $s$ .