Cool Pairs

You have two permutations of n elements, p1, p2, . . . , pn and q1, q2, . . . , qn, 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 ≤ ai, bi ≤ n.
• The permutations induce the following order: ap1 ≤ ap2 ≤ . . . ≤ apn and bq1 ≤ bq2 ≤ . . . ≤ bqn.
• A pair (i, j) is cool if i < j and ai + bj < 0. The number of cool pairs must be exactly k.

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, . . . , pn.

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

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

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.