愛ちゃんパスワード(フィボナッチ接頭辞和)
19712 ワード
ACM問題セット:https://blog.csdn.net/weixin_39778570/article/details/83187443タイトルリンク:https://code.mi.com/problem/list/view?id=137&cid=7
code
。 , A,B,C,D,mod,n 。
:
F(1) = A, F(2) = BF(1)=A,F(2)=B
F(n) = F(n-1) * F(n-2) * C^D (n >= 2)
F(n)=F(n−1)⋅F(n−2)⋅C^D (n>2)
G(n) (G(n) F(n) n ), 。
, G(n)%mod
。 6 , A, B, C, D, mod, n. (1<=A,B,C,D,mod,n<=1000000000);
2000.
------------------------------------------------------------------------------------------
n
-1
C^D ....
fa+fb-n
fa a
fb b
(f*A*n) = [fib(n), fib(n+1)] 0
n: 1 2 3 4 5 6 7 ( )
B 0 1 1 2 3 5 8 13.... Fib...
0 1 2 4 7 12 20 sumA(n-1) = f(n+1)-1 = (f*A*n)[1]-1 0
A 1 0 1 1 2 3 5 8
1 1 2 3 5 8 13 sumB(n-1) = f(n) = (f*A*n)[0]
C^D 0 0 1 2 4 7 12
0 0 1 3 7 14 26 sumC(n-1) = sumA(n-1) + sumB(n-1) - n
code
#include
#define ll long long
#define fo(i,j,n) for(register int i=j; i<=n; ++i)
using namespace std;
ll a,b,c,d,mod,n,x,MOD;
int q_pow(ll a, ll n){
int ret = 1;
while(n){
if(n&1)ret = ret*a%mod;
a = a*a%mod;
n>>=1;
}
return ret%mod;
}
int phi(int n){
int ans = n;
for(int i=2; i<=sqrt(n); i++){
if(n%i==0){
ans = ans/i*(i-1);
while(n%i==0)n/=i;
}
}
if(n>1)ans = ans/n*(n-1);
return ans;
}
void mul(int f[2], int a[2][2]){
int c[2];
memset(c,0,sizeof c);
for(int j=0; j<2; j++){
for(int k=0; k<2; k++){
c[j] = (c[j] + (ll)f[k]*a[k][j])%MOD;
}
}
memcpy(f,c,sizeof(c));
}
void mulself(int a[2][2]){
int c[2][2];
memset(c,0,sizeof(c));
for(int i=0; i<2; i++){
for(int j=0;j<2; j++){
for(int k=0; k<2; k++){
c[i][j] = (c[i][j]+(ll)a[i][k]*a[k][j])%MOD;
}
}
}
memcpy(a,c,sizeof(c));
}
void solve(){
int f[2] = {0,1};
int A[2][2] = {{0,1},{1,1}};
int t = n;
for(;t;t>>=1){
if(t&1)mul(f, A);
mulself(A);
}
// cout<
ll fa = f[0] + MOD; // f(n+1)
ll fb = f[1]-1 + MOD; // f(n+2)-1, 1
ll fc = fa + fb - n % MOD + MOD; // C^D fa+fb-n
c = q_pow(c, d%MOD+MOD); // C^D
ll ans = q_pow(a,fa)%mod * q_pow(b,fb)%mod * q_pow(c,fc)%mod;
printf("%09d
",ans);
}
int main(){
while(cin>>a>>b>>c>>d>>mod>>n){
MOD = phi(mod);
solve();
}
return 0;
}