P15306 [GeeksforGeeks] Modular multiplicative inverse 1587115620
普及-
题目描述

Given two integers ‘a’ and ‘m’. The task is to find the smallest modular multiplicative inverse of ‘a’ under modulo ‘m’.

Example 1:
Input:
a = 3
m = 11
Output: 4
Explanation: Since (43) mod 11 = 1, 4
is modulo inverse of 3. One might think,
15 also as a valid output as "(15
3)
mod 11" is also 1, but 15 is not in
ring {0, 1, 2, ... 10}, so not valid.

Example 2:
Input:
a = 10
m = 17
Output: 12
Explanation: Since (12*10) mod 17 = 1,
12 is the modulo inverse of 10.

Your Task:
You don't need to read input or print anything. Your task is to complete the function function modInverse() that takes a and m as input parameters and returns modular multiplicative inverse of ‘a’ under modulo ‘m’. If the modular multiplicative inverse doesn't exist return -1.

Expected Time Complexity : O(m)
Expected Auxilliary Space : O(1)

Constraints:
1 <= a <= 10^{4}
1 <= m <= 10^{4}

输入格式

见题面

输出格式

见题面

样例输入
a = 3 m = 11
样例输出
4