Problem:
Problem F: 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.

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.

Solution in Ruby (judge verdict: Accepted)

### main

loop do
  n, s, w, q = gets.split.map(&:to_i)
  break if (n | s | w | q) == 0

  ais = n.times.map{0}
  g = s
  for i in (0...n)
    ais[i] = (g / 7) % 10
    g = (g % 2 == 0) ? g / 2 : (g / 2) ^ w
  end  

  if q == 2 || q == 5
    nzs = 0
    count = 0
    for i in (0...n)
      nzs += 1 if ais[i] != 0
      count += nzs if ais[i] % q == 0
    end

    puts count
    next
  end
  
  mds = (n + 1).times.map{0}
  tmd = 1

  (n - 1).downto(0) do |i|
    mds[i] = (ais[i] * tmd + mds[i + 1]) % q
    tmd = (tmd * 10) % q
  end

  chash = Hash.new{0}
  chash[0] = 1
  count = 0
  
  (n - 1).downto(0) do |i|
    mdi = mds[i]
    if ais[i] != 0 && chash.include?(mdi)
      count += chash[mdi]
    end
    chash[mdi] += 1
  end
  
  puts count
end