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 ( even i = a 2i , 1 ≤ 2i ≤ n ), odd is an array consisting of the numberals whose numbers are odd in а ( odd i = a 2i - 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 b i , such that l ≤ i ≤ r and u ≤ b i ≤ v . You should print the query results modulo mod .
输入描述:
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.
输出描述:
Print m lines each containing an integer — remainder modulo mod of the query result.
示例1
输入
4 5 10000<br />2 3 4 5<br />2 4 1 3<br />1 2 2 4<br />2 3 3 5<br />1 3 3 4<br />2 5 10000<br />1 2 2 2<br />1 1 4 5<br />1 1 2 5<br />1 1 1 3<br />1 2 5 5<br />
输出
0<br />5<br />3<br />3<br />3<br />2<br />0<br />0<br />1<br />0<br />
备注:
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.
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