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## E. Hyperrook

Time limit: 1.0 second
Memory limit: 64 MB
А point of n-dimensional space is called valid if all its coordinates are integers between 0 and m − 1, inclusive. Thus, there are mn different valid points. A hyperrook can make a move from valid point a to valid point b if a and b differ in exactly one coordinate. For example, (0,2,1) → (2,2,1) → (2,2,0) → (2,1,0) represents a sequence of three moves in three-dimensional space.
A route of length d from point t0 to point td is a sequence of valid points t0, t1, …, td such that for any i from {0, 1, …, d − 1} a hyperrook can make a move from point ti to point ti + 1.
Given integers n, m, d, q and valid points t1, t2, …, tq you are to find the number of different routes of length d from ti to tj for any pair (ij) where 1 ≤ i, jq.

### Input

The first line contains five space-separated integers n (1 ≤ n ≤ 50), m (2 ≤ m ≤ 105), d (0 ≤ d ≤ 109), p (1 ≤ p ≤ 109) and q (2 ≤ q ≤ 50). Next q lines contain coordinates of points ti.

### Output

Output q lines each containing q space-separated integers. The j-th number in the i-th line should be equal to the number of different routes of length d from ti to tj modulo p.

### Samples

inputoutput
```2 8 4 10000000 4
3 5
0 5
3 7
0 0```
```896 720 720 560
720 896 560 720
720 560 896 560
560 720 560 896```
```3 3 4 10000000 3
0 2 2
1 1 1
1 2 2```
```90 36 45
36 90 54
45 54 90```
Problem Author: Petr Lezhankin
Problem Source: Ufa SATU Contest. Petrozavodsk Summer Session, August 2009
To submit the solution for this problem go to the Problem set: 1746. Hyperrook