There are M covid centres denoted by IDs 0 to M - 1 located on a cirular path (centre 1 is right to centre 0, centre 2 is right to centre 1, ... centre 0 is right to centre M - 1). Each centre can treat only one patient at a time. There are N patients and two arrays, arrival and treatment of length N is given. arrival denotes that i^th patient arrives to (i%M)^th centre on arrival[i]^th day.

If the centre is occupied, then they try getting admitted to the closest vacant centre clockwise right to the (i%M)^th centre.
If no centre is vacant, then the patient leaves.
Once admitted in a centre, the patients gets treated for treatment[i] days there and then leaves.

Output M values in which i^th value denotes the number of patients treated by i^th covid centre in total.

    Note - arrival[i] and treatment[i] is the i-th element of the array, arrival and treatment respectively. (0-indexing is followed)

Input Format -

    First line of input contains an integer , n ,denoting the number of patients and an interger, m, denoting the number of centres.

    Second line contains n space separated integers of the array, arrival.

Third line contains n space separated integers of the array, treatment.

Output Format -

Output M space seperated integers in which i^th value denotes the number of patients treated by i^th covid centre.

Constraints -

    1 ≤ N, M ≤ 10^5

    1 ≤ arrival[i], treatment[i] ≤ 10^8

    All the values of arrival are in strictly increasing order.