The task

Your code should take in an integer 0 < x < 15452417011775787851951047309563159388840946309807 and output the smallest integer m such that x^m mod 15452417011775787851951047309563159388840946309807 = 1.

You may take the input in any format that is convenient and output in any convenient form too.

Your code should take less then one minute to run on a standard desktop.

Examples

2, 7726208505887893925975523654781579694420473154903
7726208505887893925975523654781579694420473154903, 15452417011775787851951047309563159388840946309806
15452417011775787851951047309563159388840946309806, 2

You may not use any builtin or library function which solves this problem for you.

code-golf

The task

Your code should take in an integer 0 < x < 1965593254291461501637330902918203684832716283083 and output the smallest integer m such that x^m mod 1965593254291461501637330902918203684832716283083 = 1. This long number is the next prime after 2^100 so can be encoded efficiently.

You may take the input in any format that is convenient and output in any convenient form too.

Your code should take less then one minute to run on a standard desktop no matter what the input.

Examples

2, 4235851503548771316711413838489497242205033676
3, 16943406014195085266845655353957988968820134704
169434060141950852668456553539579889688, 16943406014195085266845655353957988968820134704

Those with python or similar can check the answers with e.g. pow(3,16943406014195085266845655353957988968820134704, 1965593254291461501637330902918203684832716283083) which equals 1.

You may not use any builtin or library function which solves this problem for you.

code-golf