18742번 - Avg 스페셜 저지다국어

문제

Find a sequence of steps of the following kind (if it exists) that would make all elements of any array of real numbers a₁, a₂, . . . , a_n equal:

pick k distinct indices b₁, b₂, . . . , b_k (1 ≤ b_i ≤ n) and change the values of a_b1, a_b2, . . . , a_bk to their arithmetic mean (that is, 1/k (a_b1 + a_b2 + . . . + a_bk)) simultaneously.

입력

The only line contains two integers n and k (2 ≤ k ≤ n ≤ 1000; n is divisible by k).

출력

If a required sequence of steps doesn’t exist, display a single integer −1.

Otherwise, display the number of steps in your sequence t (1 ≤ kt ≤ 10⁶), followed by t step descriptions. Each step description must consist of k distinct integers b₁, b₂, . . . , b_k (1 ≤ b_i ≤ n).

It can be shown that if a valid sequence of steps exists, a sequence satisfying kt ≤ 10⁶ exists as well.

제한

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