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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

typedef long lint;
typedef long long llint;
typedef pair<int, int> pint;
typedef pair<long long, long long> pllint;
typedef tuple<long long, long long, long long> tllint;

// static const int MAX = 1e6;
// static const int NIL = -1;
// static const llint INF = 1<<21;
// static const llint MOD = 1e9 + 7;

bool compPair(const pint& arg1, const pint& arg2) { return arg1.first > arg2.first; }
bool compTuple(const tllint& arg1, const tllint& arg2) { return get<2>(arg1) > get<2>(arg2); }
template<class T> bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

int main(void) {
    int h, w;
    cin >> h >> w;

    vector<int> a(h);
    vector<int> b(h);
    for(int ih=0;ih<h;++ih) {
        cin >> a[ih] >> b[ih]; a[ih]--; b[ih]--;
    }

    int wnow = 0, accum = 0;
    bool flg = false;
    for(int k=0;k<h;k++) {
        if(flg) { 
            cout << -1 << endl;
            continue;
        }
        if(wnow<a[k]||b[k]<wnow) {
            cout << 1 << endl;
            accum++;
        }
        else {
            accum += b[k] - wnow + 2;
            wnow = b[k] + 1;
            if(wnow<w) cout << accum << endl;
            else { 
                cout << -1 << endl;
                flg = true;
            }
        }
    }
    return 0;
}