[Nowcoder 214267] Generalized fat wave

Generalized fat wave

Title link: nowcoder 214267

To Niu Ke:

——>Click me to jump<——

Topic

Define the generalized Fibonacci sequence:
$\{\begin{array}{c}{f}_1=1\\ f_2=1\\ f_i=a\times f_{i-1}+b\times f_{i-2}(n\ge 3,n\in With)\end{array}$
Then let you find $m^{f_n}\%(1e9+7)$

Ideas

Seeing the scope of the title, we can see that it should enumerate a $n$ , then the log of other numbers, about this complexity.

Then obviously enumerate $n$ can get$f_n$, But what you want is $m^{f_n}$，$f_n$ You can't take a model, you can't be high-precision.

Then we consider not asking for $f_n$, Enum $n$ 求出 $m^{f_i}$The value of $g_i$.
Then we can see that the transfer is: $g_i=g_{i-1}^a\times g_{i-2}^b$. (That is, all calculations go to the first level)

In this way, it can be carried out in the sense of modulo without problems.

Code

#include<queue>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define mo 1000000007

using namespace std;

ll a, b, m, re, tmp, l, r;
int n;

ll ksm(ll x, ll y) {
    
    
	re = 1ll;
	while (y) {
    
    
		if (y & 1) re = (re * x) % mo;
		x = (x * x) % mo;
		y >>= 1;
	}
	return re;
}

int main() {
    
    
	scanf("%lld %lld %lld %d", &a, &b, &m, &n);
	
	l = r = m;
	for (int i = 3; i <= n; i++) {
    
    
		tmp = (ksm(l, b) % mo * ksm(r, a)) % mo;
		l = r;
		r = tmp;
	}
	
	printf("%lld", r);
	
	return 0;
}