Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

4 4
2 4
1 1
2 3
2 4

Sample Output 1

1
3
6
-1

Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

For k=1, we need one move such as (1,1) → (2,1).

For k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).

For k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).

For k=4, it is impossible to reach any square in the fifth row from the top.

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

/**
 * @param {String} raw_input 入力
 */
function Main(raw_input) {
	const [ first, ...trail ] = raw_input.split("\n");
	const [h, w] = toNumArray(first);
	const arr = toMatrix(trail, ' ').map(a1 => a1.map(a2 => parseInt(a2, 10)));
	arr.unshift(null);

	/**
	 * resultK
	 * @type Array<number>
	 */
	let resultK = new Array(h).fill(-1);
//	let minResultK = new Array(h).fill(w * h * 2);
	for (let n = 1; n <= w; n++) {
		let x = n, y = 1;
		let moveCnt = 0;
		while (true) {
			const canGoDown = !(arr[y][0] <= x && x <= arr[y][1]);

			moveCnt++;
			if (canGoDown) {
				y++;
				if (resultK[y - 2] === -1 || moveCnt < resultK[y - 2]) {
					resultK[y - 2] = moveCnt;
				}
				if (y > h) break ;
			} else {
				x++;
				if (x > w) break ;
			}
		}
		
	}
	console.log(resultK.join("\n"));
	
	
	function canGoDown(x, y) {
		const [from, to] = arr[y];
		return !(from <= x && x <= to);
	}
//	console.log(canGoDown(1, 3, arr), canGoDown(2, 3, arr), canGoDown(3, 3, arr), canGoDown(4, 3, arr));
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));

////////// ユーティリティ関数

/**
 * 文字列を数値配列
 * @param {String} str 文字列
 */
function toNumArray(str, delimitor = ' ') {
	return str.split(delimitor).map(s => parseInt(s, 10));
}

/**
 * 文字列をVigInt配列に変換する
 * @param {String} str 文字列
 */
function toBitIntArray(str, delimitor = ' ') {
	return str.split(delimitor).map(s => BigInt(s));
}

/**
 * 2次元配列を返す
 * @param {Array<String>} array 1次元の文字列配列
 * @param {String} delimitor デリミタ
 */
function toMatrix(array, delimitor = ' ') {
	const result = array.map(v => v.split(delimitor));
	return result;
}

/**
 * 合計を出す
 * @param {Array<Number>} n 数値配列
 */
function sum(n) {
	return n.reduce((a, b) => a + b);
}