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 int n, m, mod;
long long int low, high;
long long int recur(long long int left, long long int right, long long int a,
                    long long int b, long long int l, long long int r) {
  if (right <= l || r <= left) return 0;
  if (l <= left && right <= r) {
    if (high < a) return 0;
    if (a + b * (right - left - 1) < low) return 0;
    long long int LOW = (a < low) ? ((low - a - 1) / b + 1) : 0;
    long long int HIGH = min((right - left), (high - a) / b + 1);
    LOW--;
    HIGH--;
    LOW %= mod;
    HIGH %= mod;
    a %= mod;
    b %= mod;
    long long int res0 = ((LOW + 1) * (LOW) / 2) % mod;
    long long int res1 = ((HIGH + 1) * (HIGH) / 2) % mod;
    long long int res2 = (HIGH - LOW) * a;
    res0 = (res0 * b) % mod;
    res1 = (res1 * b) % mod;
    res2 = (res2) % mod;
    return (res1 - res0 + res2 + mod + mod) % mod;
  }
  long long int mid = (left + right + 1) / 2;
  long long int res0 = recur(left, mid, a, b * 2, l, r);
  long long int res1 = recur(mid, right, a + b, b * 2, l, r);
  return (res0 + res1) % mod;
}
int main() {
  cin >> n >> m >> mod;
  for (long long int i = 0; i < ((long long int)(m)); ++i) {
    long long int l, r;
    cin >> l >> r >> low >> high;
    cout << recur(0, n, 1, 1, l - 1, r) << endl;
  }
}