B"There are two bus stops denoted A and B, and there n buses that go from A to B every day. The shortest path from A to B takes t units of time but some buses might take longer paths. Moreover, buses are allowed to overtake each other during the route. At each station one can find a sorted list of moments of time when a bus is at this station. We denote this list as a_1 < a_2 < ldots < a_n for stop A and as b_1 < b_2 < ldots < b_n for stop B. The buses always depart from A and arrive to B according to the timetable, but the order in which the buses arrive may differ. Let's call an order of arrivals valid if each bus arrives at least t units of time later than departs. It is known that for an order to be valid the latest possible arrival for the bus that departs at a_i is b_{x_i} , i.e. x_i -th in the timetable. In other words, for each i there exists such a valid order of arrivals that the bus departed i -th arrives x_i -th (and all other buses can arrive arbitrary), but there is no valid order of arrivals in which the i -th departed bus arrives (x_i + 1) -th. Formally, let's call a permutation p_1, p_2, ldots, p_n valid, if b_{p_i} ge a_i + t for all i . Then x_i is the maximum value of p_i among all valid permutations. You are given the sequences a_1, a_2, ldots, a_n and x_1, x_2, ldots, x_n , but not the arrival timetable. Find out any suitable timetable for stop B b_1, b_2, ldots, b_n or determine that there is no such timetable. The first line of the input contains two integers n and t ( 1 <= q n <= q 200 ,000 , 1 <= q t <= q 10^{18} ) -- the number of buses in timetable for and the minimum possible travel time from stop A to stop B. The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= q a_1 < a_2 < ldots < a_n <= q 10^{18} ), defining the moments of time when the buses leave sto"...