The Union of k-Segments

Description:

Input:

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 10⁶) — the number of segments and the value of k.

The next n lines contain two integers l_i, r_i ( - 10⁹ ≤ l_i ≤ r_i ≤ 10⁹) each — the endpoints of the i-th segment. The segments can degenerate and intersect each other. The segments are given in arbitrary order.

Output:

First line contains integer m — the smallest number of segments.

Next m lines contain two integers a_j, b_j (a_j ≤ b_j) — the ends of j-th segment in the answer. The segments should be listed in the order from left to right.

Sample Input:

3 2
0 5
-3 2
3 8

Sample Output:

2
0 2
3 5

Sample Input:

3 2
0 5
-3 3
3 8

Sample Output:

1
0 5