I hate Shortest Path Problem

There is a grid of squares with H+1 horizontal rows and W vertical columns.

You will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \ldots, B_i-th squares from the left in the i-th row from the top.

For each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case.) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print -1 instead.

Constraints

• 1 \leq H,W \leq 2\times 10^5
• 1 \leq A_i \leq B_i \leq W

Input

Input is given from Standard Input in the following format:

H W A_1 B_1 A_2 B_2 : A_H B_H

Output

Print H lines. The i-th line should contain the answer for the case k=i.

Example

Input

4 4 2 4 1 1 2 3 2 4

Output

1 3 6 -1

inputFormat

Input

Input is given from Standard Input in the following format:

H W A_1 B_1 A_2 B_2 : A_H B_H

outputFormat

Output

Print H lines. The i-th line should contain the answer for the case k=i.

Example

Input

4 4 2 4 1 1 2 3 2 4

Output

1 3 6 -1

样例

4 4
2 4
1 1
2 3
2 4

1
3
6
-1

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