There are N contiguous cells numbered from 1 to N. Initially, each cell contains a 0 in it. A sub-contiguous group of cells can be updated this way:

1)      A range [i,j] is defined such that i < j

2)      The cell numbered i is added 1; the cell numbered i + 1 is added 2, and so on until the cell numbered j is reached and added j – i + 1

For example, if N = 7 and the updates [3, 6] and [4,7] were performed, this is what would happen.

Initially: {0,0,0,0,0,0,0}

Update [3,6]: {0,0,1,2,3,4,0}

Update [4,7]: {0,0,1,3,5,7,4}

After performing some update operations, it would be amazing to answer questions like the following:

1)      A range [u,v] is defined such that u < v

2)      The answer is the sum of every cell in the range [u,v] (both u and v are included) modulus 10,000

Given N and U updates ranges. You have to write a program capable of answering Q questions.

Input

The first line contains three integers: N (1 <= N <= 1,000,000,000), U and Q (1 <= U, Q <= 1,000), representing the number of cells, the number of update operations, and the number of questions respectively.

Each of the following U lines contains two integers i and j (1 <= i < j <= N) separated by a single space indicating an update operation.

Each of the following Q lines contains two integers u and v (1 <= u < v <= N) separated by a single space indicating a question.

Output

For each question [u,v] you must print the sum of all contiguous cells starting at u and ending at v modulus 10,000.

Example

Input:
7 2 2
3 6
4 7
4 6
1 7
Output:
15
20