Mod Inverse

문제

In many cryptographic applications, the Modular Inverse is a key point. This question involves finding the modular inverse of a number.

Given , where $xx$ and $mm$ are integers, the modular inverse of $xx$ is the unique integer $nn$, , such that the remainder upon dividing $x\times nx\; \backslash times\; n$ by $mm$ is $11$.

For example, $4\times 13=52=17\times 3+14\; \backslash times\; 13\; =\; 52\; =\; 17\; \backslash times\; 3\; +\; 1$, so the remainder when $5252$ is divided by $1717$ is $11$, and thus $1313$ is the inverse of $44$ modulo $1717$.

You are to write a program which accepts as input the two integers $xx$ and $mm$, and outputs either the modular inverse $nn$, or the statement No such integer exists. if there is no such integer $nn$.