Problem Statement

You are given a string $S$ of length $N$ and a string $T$ of length $M$, both consisting of digits from 1 to 9.

You will perform the following operation for $k=1,2,\ldots,M$ in order:

• Choose an integer $i$ such that $1 \le i \le N$. Then, replace the $i$-th character of $S$ with the $k$-th character of $T$.

Find the maximum possible value of the resulting string $S$ interpreted as an integer after performing the $M$ operations.

Constraints

• $1 \le N,M \le 10^6$
• $N$ and $M$ are integers.
• $S$ is a string of length $N$ consisting of digits from 1 through 9.
• $T$ is a string of length $M$ consisting of digits from 1 through 9.

Input

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

N M
S
T

Output

Print the maximum possible value of the resulting string $S$ interpreted as an integer after performing the $M$ operations.