# Find the Multiples

Time Limit : 8 sec, Memory Limit : 131072 KB

# Problem F: Find the Multiples

You are given a sequence a0a1...aN-1 digits and a prime number Q. For each ij with ai ≠ 0, the subsequence aiai+1...aj can be read as a decimal representation of a positive integer. Subsequences with leading zeros are not considered. Your task is to count the number of pairs (i, j) such that the corresponding subsequence is a multiple of Q.

## Input

The input consists of at most 50 datasets. Each dataset is represented by a line containing four integers N, S, W, and Q, separated by spaces, where 1 ≤ N ≤ 105, 1 ≤ S ≤ 109, 1 ≤ W ≤ 109, and Q is a prime number less than 108. The sequence a0...aN-1 of length N is generated by the following code, in which ai is written as a[i].

```    int g = S;
for(int i=0; i<N; i++) {
a[i] = (g/7) % 10;
if( g%2 == 0 ) { g = (g/2); }
else           { g = (g/2) ^ W; }
}
```

Note: the operators /, %, and ^ are the integer division, the modulo, and the bitwise exclusiveor, respectively. The above code is meant to be a random number generator. The intended solution does not rely on the way how the sequence is generated.

The end of the input is indicated by a line containing four zeros separated by spaces.

## Output

For each dataset, output the answer in a line. You may assume that the answer is less than 230.

## Sample Input

```3 32 64 7
4 35 89 5
5 555 442 3
5 777 465 11
100000 666 701622763 65537
0 0 0 0
```

## Output for the Sample Input

```2
4
6
3
68530
```

In the first dataset, the sequence is 421. We can find two multiples of Q = 7, namely, 42 and 21.

In the second dataset, the sequence is 5052, from which we can find 5, 50, 505, and 5 being the multiples of Q = 5. Notice that we don't count 0 or 05 since they are not a valid representation of positive integers. Also notice that we count 5 twice, because it occurs twice in different positions.

In the third and fourth datasets, the sequences are 95073 and 12221, respectively.

Source: ACM International Collegiate Programming Contest , Asia Regional Tokyo, Tokyo, Japan, 2010-12-12
http://icpc2010.honiden.nii.ac.jp/