A positive integer multiplied times its inverse is always equal to 1: 17*(1/17)==1. Modular arithmetic has a similar inverse function, although, for modulus m, we are confined to integers from 0 to m-1. The modular multiplicative inverse of 3 modulus 5 is equal to 2 because (3*2)%5==1. Another example: the modular inverse of 17 modulus 1000007 is equal to 58824 because (17*58824)%1000007==1. The modular inverse, if it exists, must always be in the range 0 to m-1.

Create a function that has arguments integer n and modulus m. The function will return the modular inverse of n mod m. If the modular inverse does not exist, return False.

Examples

mod_inv(2, 3) ➞ 2

mod_inv(12, 47) ➞ 4

mod_inv(11, 33) ➞ False

mod_inv(55, 678) ➞ 37

mod_inv(81, 3455) ➞ 2346

Notes

• Some of the test cases have rather large integers, so if you attempt to do a brute force search of the entire modular field, you may not be successful due to the 12 second time limit imposed by the server. See Resources for a more efficient approach.
• The modular inverse of a number n modulus m exists only if n and m are coprime (i.e. they have no common factors other than 1).
• One practical use of modular inverse is in public-key cryptography like RSA where it can be used to determine the value of the private key.