## PWSUMC - Power Sum

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Some people may found PWSUM a too easy problem. We propose here some serious constraints. ### Input

The input contains several lines, you don't have to process all, it may be impossible, only all first ones you are able to, in the given time. Each line contains two integers : N, and P, a prime number.

### Output

For the kth line, print Sum(i^k for i in [1..N]).
As the answer could not fit in a 64-bit container, just output your answer modulo P.
The difficulty will seriously increase as you will process lines.

### Example

```Input:
2 5
3 7
2 13
[...] some more lines
```
```Output:
3
0
9
[...] as many as you can.
```

### Explanations

For the first line : 1^1 + 2^1 = 3 (mod).
For the second line : 1^2 + 2^2 + 3^2 = 14 = 0 (mod)
For the third line : 1^3 + 2^3 = 9 (mod).

### Constraints

```0 < N <= 10^9
1 < P <= 10^9, a prime number
```

The numbers N are uniform randomly chosen. The prime numbers P are log-uniform randomly chosen.
The challenge is to be the fastest. There are 100000 lines, one point per case.
Constraints allow everybody to get some points.
Have fun ;-)

hide comments abdou_93: 2014-06-12 22:11:12 your problems are really awesome . can you tell me a book that you prefer to read it.(thanks Francky) --ans(Francky)--> I don't have any books, here it's a very common task. (Obviously, I have some maths books from my studies, but I didn't use them specifically in any problem). I don't think my problems are awesome, it's most of them reload of common task. Few of them are 100% genuine, it's true ; eg: HAL9000, MOON2. @Francky-thanks for reply Last edit: 2014-06-13 13:20:39 THE_SCORPION: 2014-04-26 11:39:36 Any hint to solve it ? --ans(Francky)--> hint Last edit: 2014-04-26 15:24:44

 Added by: Francky Date: 2014-03-23 Time limit: 25s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 Resource: Own Problem