18449번 - Cool Pairs 스페셜 저지다국어

문제

You have two permutations of n elements, p₁, p₂, . . . , p_n and q₁, q₂, . . . , q_n, and one integer k.

You need to find two integer arrays, a and b, with the following properties:

• The elements of the arrays must be integers such that −n ≤ a_i, b_i ≤ n.
• The permutations induce the following order: a_p1 ≤ a_p2 ≤ . . . ≤ a_pn and b_q1 ≤ b_q2 ≤ . . . ≤ b_qn.
• A pair (i, j) is cool if i < j and a_i + b_j < 0. The number of cool pairs must be exactly k.

입력

The first line of the input contains two integers n and k: the number of elements and the required number of cool pairs (1 ≤ n ≤ 300 000, 0 ≤ k ≤ n·(n−1)/2).

The second line contains n space-separated integers: the permutation p₁, p₂, . . . , p_n.

The third line contains n space-separated integers: the permutation q₁, q₂, . . . , q_n.

It is guaranteed that each integer from 1 to n appears exactly once in each permutation.

출력

If there is no such pair of integer arrays that the number of cool pairs is equal to k, print “No” on a single line.

Otherwise, print “Yes” on the first line, and print the arrays a and b on the next two lines. Separate array elements by spaces.

제한

힌트