Dress'em in Vests!

Description:

Input:

The first input line contains four integers n, m, x and y (1 ≤ n, m ≤ 10⁵, 0 ≤ x, y ≤ 10⁹) — the number of soldiers, the number of vests and two numbers that specify the soldiers' unpretentiousness, correspondingly.

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹) in non-decreasing order, separated by single spaces — the desired sizes of vests.

The third line contains m integers b₁, b₂, ..., b_m (1 ≤ b_j ≤ 10⁹) in non-decreasing order, separated by single spaces — the sizes of the available vests.

Output:

In the first line print a single integer k — the maximum number of soldiers equipped with bulletproof vests.

In the next k lines print k pairs, one pair per line, as "u_i v_i" (without the quotes). Pair (u_i, v_i) means that soldier number u_i must wear vest number v_i. Soldiers and vests are numbered starting from one in the order in which they are specified in the input. All numbers of soldiers in the pairs should be pairwise different, all numbers of vests in the pairs also should be pairwise different. You can print the pairs in any order.

If there are multiple optimal answers, you are allowed to print any of them.

Sample Input:

5 3 0 0
1 2 3 3 4
1 3 5

Sample Output:

2
1 1
3 2

Sample Input:

3 3 2 2
1 5 9
3 5 7

Sample Output:

3
1 1
2 2
3 3

Note:

In the first sample you need the vests' sizes to match perfectly: the first soldier gets the first vest (size 1), the third soldier gets the second vest (size 3). This sample allows another answer, which gives the second vest to the fourth soldier instead of the third one.

In the second sample the vest size can differ from the desired size by at most 2 sizes, so all soldiers can be equipped.