A. Polo the Penguin and Segments
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

Little penguin Polo adores integer segments, that is, pairs of integers [lr] (l ≤ r).

He has a set that consists of n integer segments: [l 1r 1], [l 2r 2], ..., [l nr n]. We know that no two segments of this set intersect. In one move Polo can either widen any segment of the set 1 unit to the left or 1 unit to the right, that is transform [lr] to either segment [l - 1; r], or to segment [lr + 1].

The value of a set of segments that consists of n segments [l 1r 1], [l 2r 2], ..., [l nr n] is the number of integers x, such that there is integer j, for which the following inequality holds, l j ≤ x ≤ r j.

Find the minimum number of moves needed to make the value of the set of Polo's segments divisible by k.


The first line contains two integers n and k (1 ≤ n, k ≤ 105). Each of the following n lines contain a segment as a pair of integers l i and r i ( - 105 ≤ l i ≤ r i ≤ 105), separated by a space.

It is guaranteed that no two segments intersect. In other words, for any two integers i, j (1 ≤ i < j ≤ n) the following inequality holds, min(r i, r j) < max(l i, l j).


In a single line print a single integer — the answer to the problem.

2 3
1 2
3 4
3 7
1 2
3 3
4 7