Exponential modulus algorithm

Topic:

Given a A, b

Find out: A^a^a....^a (b a)

Input:

A, b

Output

Result of Operation

Examples:

2 3

Output: 16

Range: a,b<=10^9

We can get the answer first: ans=a^ (a^ (b-1))

However (a^ (b-1)) as the exponent is too big, must take the model

Make y= (a^ (b-1)), p=1e9+7

Y=k*φ (P) + (y%φ (p))

Because x^φ (p)ξ1 (mod p)

So a^φ (p)%p=1

So a^y=a^ (y%φ (p))

Because p is a prime number, φ (p) =p-1

So the a^ (b-1) mode p-1

You can do it with a quick power.

1#include <cstdio>2#include <iostream>3#include <algorithm>4#include <cstring>5 using namespacestd;6 intMod=1000000007;7 Long Longa,b,ans,s;8 Long LongQpow (Long LongXintYintmo)9 {Ten   Long Longres=1; One    while(y) A     { -       if(y&1) res= (res*x)%mo; -x= (x*x)%mo; they>>=1; -     } -   returnRes; - } + intMain () - { +Cin>>a>>b; AS=qpow (a,b-1, mod-1); atans=Qpow (a,s,mod); -cout<<ans; -}

Exponential modulus algorithm