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

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline

def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    inf=10**7
    class LazySegTree:
        def __init__(self, A, initialize=True, segfunc=min, ident=inf):
            self.N = len(A)
            self.LV = (self.N - 1).bit_length()
            self.N0 = 1 << self.LV
            self.segfunc = segfunc
            self.ident = ident
            if initialize:
                self.data = [self.ident] * self.N0 + A + [self.ident] * (self.N0 - self.N)
                for i in range(self.N0 - 1, 0, -1):
                    self.data[i] = segfunc(self.data[i * 2], self.data[i * 2 + 1])
            else:
                self.data = [self.ident] * (self.N0 * 2)
            self.lazy = [0] * (self.N0 * 2)
            self.lazy_flg = [False] * (self.N0 * 2)
 
        def _ascend(self, i):
            for _ in range(i.bit_length() - 1):
                i >>= 1
                self.data[i] = self.segfunc(self.data[i * 2], self.data[i * 2 + 1])
 
        def _descend(self, idx):
            lv = idx.bit_length()
            block_size = 2**self.LV
            for j in range(lv - 1, 0, -1):
                i = idx >> j
                block_size >>= 1
                x = self.lazy[i]
                if not self.lazy_flg[i]:
                    continue
                self.lazy_flg[i] = False
                self.lazy[i * 2] = x
                self.lazy[i * 2 + 1] = x + block_size
                self.lazy_flg[i * 2] = True
                self.lazy_flg[i * 2 + 1] = True
                self.data[i * 2] = x
                self.data[i * 2 + 1] = x + block_size
 
        # open interval [l, r)
        def update(self, l, r, x):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            l_ori = l
            r_ori = r
            xl = x
            xr = x + (r-l)
            block_size = 1
            while l < r:
                if l & 1:
                    self.data[l] = xl
                    self.lazy[l] = xl
                    self.lazy_flg[l] = True
                    l += 1
                    xl += block_size
                if r & 1:
                    r -= 1
                    xr -= block_size
                    self.data[r] = xr
                    self.lazy[r] = xr
                    self.lazy_flg[r] = True
                l >>= 1
                r >>= 1
                block_size <<= 1
            self._ascend(l_ori // (l_ori & -l_ori))
            self._ascend(r_ori // (r_ori & -r_ori) - 1)
 
        # open interval [l, r)
        def query(self, l, r):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            ret = self.ident
            while l < r:
                if l & 1:
                    ret = self.segfunc(ret, self.data[l])
                    l += 1
                if r & 1:
                    ret = self.segfunc(self.data[r - 1], ret)
                    r -= 1
                l >>= 1
                r >>= 1
            return ret

    ##########
    H, W = MI()
    ST = LazySegTree([inf] + [0] * W)
    for h in range(H):
        a, b = MI()
        ST.update(a+1, b+2, ST.query(a, a+1)+1)
        
        # L=[]
        # for i in range(W+2):
        #     L.append(ST.query(i, i+1))
        # print(L)
        
        ans = ST.query(2, W+2)
        if ans >= inf:
            print(-1)
        else:
            print(h + 1 + ans)


    mod=10**9+7

main()