题目链接
1 #include<bits/stdc++.h>
2 using namespace std;
3 #define e exp(1)
4 #define pi acos(-1)
5 #define mod 1000000007
6 #define inf 0x3f3f3f3f
7 #define ll long long
8 #define ull unsigned long long
9 #define mem(a,b) memset(a,b,sizeof(a))
10 int gcd(int a,int b){return b?gcd(b,a%b):a;}
11
12 ll A,B,C,D,N,P;
13 struct mat {
14 ll a[3][3];
15 }c;
16
17 mat mat_mul(mat x,mat y) {
18 mat s;
19 mem(s.a,0);
20 for(int i=0;i<3;i++)
21 for(int j=0;j<3;j++)
22 for(int k=0;k<3;k++)
23 s.a[i][j]=(s.a[i][j]+x.a[i][k]*y.a[k][j]%mod)%mod;
24 return s;
25 }
26
27 mat mat_pow(ll n) {
28 mat res;
29 mem(res.a,0);
30 res.a[0][0]=res.a[1][1]=res.a[2][2]=1;
31 while(n) {
32 if(n&1) res=mat_mul(res,c);
33 c=mat_mul(c,c);
34 n>>=1;
35 }
36 return res;
37 }
38
39 ll solove(ll i) {
40 ll l=i,r=N;
41 ll p=P/i;
42 while(l<r) {
43 int mid=r-(r-l)/2;
44 if(p==P/mid) l=mid;
45 else if(p>P/mid)r=mid-1;
46 else l=mid+1;
47 }
48 return l;
49 }
50
51 int main() {
52 int T;scanf("%d",&T);
53 while(T--) {
54 scanf("%lld%lld%lld%lld%lld%lld",&A,&B,&C,&D,&P,&N);
55 if(N==1){printf("%lld\n",A);continue;}
56 if(N==2){printf("%lld\n",B);continue;}
57 ll f1=B; ll f2=A; mat ans;
58 for(ll i=3; i<=N;) {
59 ll j=solove(i);
60 mem(c.a,0);
61 c.a[0][0]=D;c.a[0][1]=C;
62 c.a[2][2]=1;c.a[1][0]=1;
63 c.a[0][2]=P/i; ans=mat_pow(j-i+1);
64 ll ff1=(ans.a[0][0]*f1%mod+ans.a[0][1]*f2%mod+ans.a[0][2])%mod;
65 ll ff2=(ans.a[1][0]*f1%mod+ans.a[1][1]*f2%mod+ans.a[1][2])%mod;
66 f1=ff1; f2=ff2; i=j+1;
67 }
68 printf("%lld\n",f1);
69 }
70 return 0;
71 }
