Buggy python submission (verdict: Time Limit Exceeded):
# 写経
# https://atcoder.jp/contests/abc177/submissions/16463802

import numpy as np
i4 = np.int32
i8 = np.int64
  
def solve(a, b, H, W):
    ret = np.empty(H, i8)
    for i in range(H):
        ret[i] = -1
    dp0 = np.arange(W)
    dp = np.arange(W)
    arg0 = W - 1
    arg = 0
    for i in range(H):
        r1 = np.searchsorted(dp, a[i])
        r2 = np.searchsorted(dp, b[i])
        if b[i] == W: #右端まで壁が続く場合
            if r1 == 0:
                return ret
            else:
                dp0 = dp0[: r1] #壁があるところより先は無視する
                dp = dp[: r1]
        else:
            dp[r1:r2] = b[i] #合流させる
 
        if arg0 > -1:   #直進する流れが残っている場合
            if r1 <= arg0 < r2: #壁がある場合
                for j in range(r1 - 1, -1, -1):
                    if dp[j] == dp0[j]: 
                        arg0 = j    #ここまで直進してきた他の流れに乗り換える
                        ret[i] = i + 1
                        break
                else:
                    arg0 = -1
                    arg = np.argmin(dp - dp0) #残っている値の中での最小値
                    ret[i] = dp[arg] - dp0[arg] + i + 1
            else:
                ret[i] = i + 1
        else: 
            if r1 <= arg < r2:
                arg = np.argmin(dp - dp0)
            ret[i] = dp[arg] - dp0[arg] + i + 1
        
        """
        if i % 1000 == 999:
            m = 0
            prev = dp[0]
            for k in range(1, dp.shape[0]):
                if dp[k] > prev:
                    dp0[m] = dp0[k - 1]
                    dp[m] = prev
                    m += 1
                    prev = dp[k]
            else:
                dp0[m] = dp0[dp0.shape[0] - 1]
                dp[m] = prev
                m += 1
            dp0 = dp0[: m]
            dp = dp[: m]
            if arg0 > -1:
                for j in range(m - 1, -1, -1):
                    if dp[j] == dp0[j]:
                        arg0 = j
                        break
            else:
                arg = np.argmin(dp - dp0)
        """
    return ret
 
 
def main(in_file):
    stdin = open(in_file)
    H, W = [int(x) for x in stdin.readline().split()]
    ab = np.fromstring(stdin.read(), i8, sep=' ').reshape((-1, 2)).T.copy()
    ans = solve(ab[0] - 1, ab[1], H, W)
    p = '\n'.join([str(x) for x in ans.tolist()])
    print(p)
 
 
def cc_export():
    from numba.pycc import CC
    from numba.types import Array, int64
    cc = CC('my_module')
    cc.export('solve', (Array(int64, 1, 'C'), Array(int64, 1, 'C'), int64, int64))(solve)
    cc.compile()
 
 
if __name__ == '__main__':
    import sys
    if sys.argv[-1] == 'ONLINE_JUDGE':
        cc_export()
        exit(0)
    from my_module import solve
    main('/dev/stdin')

Fixed submission:
# 写経
# https://atcoder.jp/contests/abc177/submissions/16463802

import numpy as np
i4 = np.int32
i8 = np.int64
  
def solve(a, b, H, W):
    ret = np.empty(H, i8)
    for i in range(H):
        ret[i] = -1
    dp0 = np.arange(W) #初期位置
    dp = np.arange(W) #現在位置
    arg0 = W - 1
    arg = 0
    for i in range(H):
        r1 = np.searchsorted(dp, a[i])
        r2 = np.searchsorted(dp, b[i])
        if b[i] == W: #右端まで壁が続く場合
            if r1 == 0:
                return ret
            else:
                dp0 = dp0[: r1] #壁があるところより先は無視する
                dp = dp[: r1]
        else:
            dp[r1:r2] = b[i] #合流させる
 
        if arg0 > -1:   #直進する流れが残っている場合
            if r1 <= arg0 < r2: #壁がある場合
                for j in range(r1 - 1, -1, -1):
                    if dp[j] == dp0[j]: 
                        arg0 = j    #ここまで直進してきた他の流れに乗り換える
                        ret[i] = i + 1
                        break
                else:
                    arg0 = -1
                    arg = np.argmin(dp - dp0) #残っている値の中での最小値
                    ret[i] = dp[arg] - dp0[arg] + i + 1
            else:
                ret[i] = i + 1
        else: 
            if r1 <= arg < r2:
                arg = np.argmin(dp - dp0)
            ret[i] = dp[arg] - dp0[arg] + i + 1
        
        
        if i % 1000 == 999:
            m = 0
            prev = dp[0]
            for k in range(1, dp.shape[0]):
                if dp[k] > prev: #dp[0]とは別の流れにあるものについて
                    dp0[m] = dp0[k - 1] #最小のずれを持つもののみ残してまとめる
                    dp[m] = prev 
                    m += 1
                    prev = dp[k]
            else: #流れが一つのみの場合はこの流れの実を追いかける
                dp0[m] = dp0[dp0.shape[0] - 1]
                dp[m] = prev
                m += 1
            dp0 = dp0[: m]
            dp = dp[: m]
            if arg0 > -1: #現在最小である流れなどの情報も更新しておく
                for j in range(m - 1, -1, -1):
                    if dp[j] == dp0[j]:
                        arg0 = j
                        break
            else:
                arg = np.argmin(dp - dp0)
        
    return ret
 
 
def main(in_file):
    stdin = open(in_file)
    H, W = [int(x) for x in stdin.readline().split()]
    ab = np.fromstring(stdin.read(), i8, sep=' ').reshape((-1, 2)).T.copy()
    ans = solve(ab[0] - 1, ab[1], H, W)
    p = '\n'.join([str(x) for x in ans.tolist()])
    print(p)
 
 
def cc_export():
    from numba.pycc import CC
    from numba.types import Array, int64
    cc = CC('my_module')
    cc.export('solve', (Array(int64, 1, 'C'), Array(int64, 1, 'C'), int64, int64))(solve)
    cc.compile()
 
 
if __name__ == '__main__':
    import sys
    if sys.argv[-1] == 'ONLINE_JUDGE':
        cc_export()
        exit(0)
    from my_module import solve
    main('/dev/stdin')