Fun With Functions
Limits
1s, 512 MB
Let's define a function f:
f(x)=ax+b We know, f2(x)=f(f(x)) and f3(x)=f(f(f(x))). We can write a generalized form, fn(x)=f(fn−1(x)), where n>1.
You will be given five integers: a, b, n, m, and MOD. Find the value of ∑x=1mfn(x). As the answer can be huge, print it modulo MOD.
Input
First line contains an integer t (1≤t≤100000), denoting the number of testcases.
Each tescase contains five integers a,b, n, m and MOD.
For all subtasks, 1≤a,b,m≤109.
Subtasks:
- Subtask 1 (10 points): n=1, 2≤MOD≤109+7
- Subtask 2 (30 points): 1≤n≤109, MOD=109+7
- Subtask 3 (60 points): 1≤n≤109, 2≤MOD≤109+7
Output
For each testcase, print the answer in a separate line.
Sample
Input | Output |
---|
4
2 3 1 1 100000000
2 3 1 3 100000000
1 3 1 3 100000000
2 3 2 3 100000000
| 5
21
15
51
|