Dasha logged into the system and began to solve problems. One of them is as follows:

Given two sequences a and b of length n each you need to write a sequence c of length n, the i-th element of which is calculated as follows: c_i = b_i - a_i.

About sequences a and b we know that their elements are in the range from l to r. More formally, elements satisfy the following conditions: l ≤ a_i ≤ r and l ≤ b_i ≤ r. About sequence c we know that all its elements are distinct.

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Dasha wrote a solution to that problem quickly, but checking her work on the standard test was not so easy. Due to an error in the test system only the sequence a and the compressed sequence of the sequence c were known from that test.

Let's give the definition to a compressed sequence. A compressed sequence of sequence c of length n is a sequence p of length n, so that p_i equals to the number of integers which are less than or equal to c_i in the sequence c. For example, for the sequence c = [250, 200, 300, 100, 50] the compressed sequence will be p = [4, 3, 5, 2, 1]. Pay attention that in c all integers are distinct. Consequently, the compressed sequence contains all integers from 1 to n inclusively.

Help Dasha to find any sequence b for which the calculated compressed sequence of sequence c is correct.

Input

The first line contains three integers n, l, r (1 ≤ n ≤ 10⁵, 1 ≤ l ≤ r ≤ 10⁹) — the length of the sequence and boundaries of the segment where the elements of sequences a and b are.

The next line contains n integers a₁, a₂, ..., a_n (l ≤ a_i ≤ r) — the elements of the sequence a.

The next line contains n distinct integers p₁, p₂, ..., p_n (1 ≤ p_i ≤ n) — the compressed sequence of the sequence c.

Output

If there is no the suitable sequence b, then in the only line print "-1".

Otherwise, in the only line print n integers — the elements of any suitable sequence b.

Note

Sequence b which was found in the second sample is suitable, because calculated sequence c = [2 - 3, 2 - 4, 2 - 8, 9 - 9] = [ - 1, - 2, - 6, 0] (note that c_i = b_i - a_i) has compressed sequence equals to p = [3, 2, 1, 4].

Dasha and Very Difficult Problem

Examples