D - Match or Not

Score : $400$ points

Problem Statement

You are given strings $S$ and $T$ consisting of lowercase English letters and ?. Here, $|S| \gt |T|$ holds (for a string $X$, $|X|$ denotes the length of $X$).

Two strings $X$ and $Y$ such that $|X|=|Y|$ is said to match if and only if:

• one can make $X$ equal $Y$ by replacing each ? in $X$ and $Y$ with any English letter independently.

Solve the following problem for each $x=0,1,\ldots,|T|$:

• Let $S'$ be the string of length $|T|$ obtained by concatenating the first $x$ characters and the last $(|T|-x)$ characters of $S$ without changing the order. Print Yes if $S'$ and $T$ match, and No otherwise.

Constraints

• $S$ and $T$ are strings consisting of lowercase English letters and ?.
• $1 \leq |T| \lt |S| \leq 3 \times 10^5$

Input

The input is given from Standard Input in the following format:

$S$

$T$

Output

Print $(|T|+1)$ lines.
The $i$-th line should contain the answer for $x=i-1$.

a?c
b?

Yes
No
No

When $x=0$, $S'$ equals ?c. Here, we can replace the $1$-st character of $S'$, ?, with b and the $2$-nd character of $T$, ?, with c to make $S'$ equal $T$, so $S'$ and $T$ match. Thus, Yes should be printed in the first line.
When $x=1$ and $2$, respectively, $S'$ is ac and a?, neither of which matches with $T$. Thus, No should be printed in the second and third lines.

atcoder
?????

Yes
Yes
Yes
Yes
Yes
Yes

beginner
contest

No
No
No
No
No
No
No
No