Find the Multiples

You are given a sequence a0a1...aN-1 digits and a prime number Q. For each i ≤ j 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.

Example

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

2 4 6 3 68530

inputFormat

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.

outputFormat

Output

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

Example

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

2 4 6 3 68530

样例

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

2
4
6
3
68530

</p>