CF289A.Polo the Penguin and Segments

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

He has a set that consists of n integer segments: [_l_1; _r_1], [_l_2; _r_2], ..., [l__n; r__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 [l; r] to either segment [l - 1; r], or to segment [l; r + 1].

The value of a set of segments that consists of n segments [_l_1; _r_1], [_l_2; _r_2], ..., [l__n; r__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.

小企鹅 Polo 非常喜爱整数线段，即形如 ([l, r])（其中 (l \leq r)）的整数对。

他拥有一个由 (n) 个整数线段组成的集合：([l_1, r_1],\ [l_2, r_2],\ \dots,\ [l_n, r_n])。已知该集合中任意两个线段互不相交。在一次操作中，Polo 可以将集合中的任意一个线段向左扩展 1 单位或向右扩展 1 单位，即把 ([l, r]) 变为 ([l - 1, r]) 或 ([l, r + 1])。

由 (n) 个线段 ([l_1, r_1],\ [l_2, r_2],\ \dots,\ [l_n, r_n]) 构成的线段集合的值，定义为满足如下条件的整数 (x) 的个数：存在某个整数 (j)，使得不等式 (l_j \leq x \leq r_j) 成立。

求使 Polo 的线段集合的值能被 (k) 整除所需的最少操作次数。

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).

第一行包含两个整数 $n$ 和 $k$（$1 \leq n, k \leq 10^5$）。接下来的 $n$ 行每行包含一个线段，由一对整数 $l_i$ 和 $r_i$（$-10^5 \leq l_i \leq r_i \leq 10^5$）表示，两个整数之间用空格分隔。

保证任意两个线段互不相交。换言之，对任意两个整数 $i, j$（$1 \leq i < j \leq n$），均满足以下不等式：$\min(r_i, r_j) < \max(l_i, l_j)$。

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

在一行中输出一个整数——该问题的答案。