You are given a sequence a0a1 · · · aN−1 of 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.

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 ≤ 10^5, 1 ≤ S ≤ 10^9, 1 ≤ W ≤ 10^9, and Q is a prime number less than 10^8. 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.

For each dataset, output the answer in a line. You may assume that the answer is less than 2^30.

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.

Asia 2010, Japan