Bobo is tired of all kinds of hard LIS (Longest Increasing Subsequence) problems,
so he decides to make himself some easier one.

Bobo has n pairs
where holds for all i.
He defines f(i, j) be the length of longest increasing subsequence of sequence .

It's clear that .
Bobo would like to know g(k) which is the number of pairs (i, j) where f(i, j) = k.

Note that a sequence labeled with is an increasing subsequence of only if:

*
*

The input contains at most 30 sets. For each set:
The first line contains 2 integers n, m ().
The i-th of the following n lines contains 2 integers  ().

For each set, 4 integers g(1), g(2), g(3), g(4).

2 4
1 2
3 4

0 3 0 1

2 1
1 1
1 1

4 0 0 0