Goffi and Squary Partition

Recently, Goffi is interested in squary partition of integers.

A set \(X\) of \(k\) distinct positive integers is called squary partition of \(n\) if and only if it satisfies the following conditions:
[ol]

the sum of \(k\) positive integers is equal to \(n\)

one of the subsets of \(X\) containing \(k - 1\) numbers sums up to a square of integer.

[/ol]
For example, a set {1, 5, 6, 10} is a squary partition of 22 because 1 + 5 + 6 + 10 = 22 and 1 + 5 + 10 = 16 = 4 × 4.

Goffi wants to know, for some integers \(n\) and \(k\), whether there exists a squary partition of \(n\) to \(k\) distinct positive integers.

Input contains multiple test cases (less than 10000). For each test case, there's one line containing two integers \(n\) and \(k\) (\(2 \le n \le 200000, 2 \le k \le 30\)).

For each case, if there exists a squary partition of \(n\) to \(k\) distinct positive integers, output "YES" in a line. Otherwise, output "NO".

2 2
4 2
22 4

NO
YES
YES

BestCoder Round #6