# Goffi and Squary Partition

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

## Description

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

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

## Output

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

## Sample Input

2 2
4 2
22 4

## Sample Output

NO
YES
YES

heyang

## Source

BestCoder Round #6