Problem: Let a be an array consisting of n numbers. The array's elements are numbered from 1 to n, even is an array consisting of the numerals whose numbers are even in a (eveni = a2i, 1 ≤ 2i ≤ n), odd is an array consisting of the numberals whose numbers are odd in а (oddi = a2i - 1, 1 ≤ 2i - 1 ≤ n). Then let's define the transformation of array F(a) in the following manner:

  * if n > 1, F(a) = F(odd) + F(even), where operation " + " stands for the arrays' concatenation (joining together) 
  * if n = 1, F(a) = a



Let a be an array consisting of n numbers 1, 2, 3, ..., n. Then b is the result of applying the transformation to the array a (so b = F(a)). You are given m queries (l, r, u, v). Your task is to find for each query the sum of numbers bi, such that l ≤ i ≤ r and u ≤ bi ≤ v. You should print the query results modulo mod.

Input

The first line contains three integers n, m, mod (1 ≤ n ≤ 1018, 1 ≤ m ≤ 105, 1 ≤ mod ≤ 109). Next m lines describe the queries. Each query is defined by four integers l, r, u, v (1 ≤ l ≤ r ≤ n, 1 ≤ u ≤ v ≤ 1018).

Please do not use the %lld specificator to read or write 64-bit integers in C++. Use %I64d specificator.

Output

Print m lines each containing an integer — remainder modulo mod of the query result.

Examples

Input

4 5 10000
2 3 4 5
2 4 1 3
1 2 2 4
2 3 3 5
1 3 3 4


Output

0
5
3
3
3


Input

2 5 10000
1 2 2 2
1 1 4 5
1 1 2 5
1 1 1 3
1 2 5 5


Output

2
0
0
1
0

Note

Let's consider the first example. First let's construct an array b = F(a) = F([1, 2, 3, 4]). 

  * Step 1. F([1, 2, 3, 4]) = F([1, 3]) + F([2, 4])
  * Step 2. F([1, 3]) = F([1]) + F([3]) = [1] + [3] = [1, 3]
  * Step 3. F([2, 4]) = F([2]) + F([4]) = [2] + [4] = [2, 4]
  * Step 4. b = F([1, 2, 3, 4]) = F([1, 3]) + F([2, 4]) = [1, 3] + [2, 4] = [1, 3, 2, 4]

Thus b = [1, 3, 2, 4]. Let's consider the first query l = 2, r = 3, u = 4, v = 5. The second and third positions in the array b do not have numbers in the range [4, 5], so the sum obviously equals zero. Let's consider the second query l = 2, r = 4, u = 1, v = 3. The second and third positions have two numbers that belong to the range [1, 3], their sum equals 5.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long n, m, mod;
long long gp(long long lo, long long hi, long long br) {
  if (lo > hi) return 0;
  if (br & 1)
    return ((((lo + hi) / 2) % mod) * (br % mod)) % mod;
  else
    return (((lo + hi) % mod) * ((br / 2) % mod)) % mod;
}
long long sum(long long beg, long long d, long long br, long long lo,
              long long hi) {
  long long end = beg + (br - 1) * d;
  if (end > hi) {
    end -= ((end - hi) / d) * d;
    if (end > hi) end -= d;
  }
  if (beg < lo) {
    beg += ((lo - beg) / d) * d;
    if (beg < lo) beg += d;
  }
  return gp(beg, end, (end - beg) / d + 1);
}
long long f(long long beg, long long d, long long br, long long l, long long r,
            long long lo, long long hi) {
  if (br <= 0 || l > r || br < l) return 0;
  if (l == 1 && br <= r) return sum(beg, d, br, lo, hi);
  long long brc = br / 2, brn = br - brc;
  return (f(beg, 2 * d, brn, l, min(r, brn), lo, hi) +
          f(beg + d, 2 * d, brc, max(l, brn + 1) - brn, r - brn, lo, hi)) %
         mod;
}
int main() {
  scanf("%I64d %I64d %I64d", &n, &m, &mod);
  while (m--) {
    long long a, b, c, d;
    scanf("%I64d %I64d %I64d %I64d", &a, &b, &c, &d);
    printf("%I64d\n", f(1, 1, n, a, b, c, d));
  }
  return 0;
}