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

    Hint

    heyang

    Source

    BestCoder Round #6

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