Given an $N \times M$ chessboard, initially, all positions on the board are empty.

Not a Little Blue Fish wants to perform several operations. Each operation is as follows:

1. Choose an empty cell $(i, j)$.
2. Let $x$ be the smallest positive integer that has not yet appeared in the row or column containing $(i, j)$.
3. Fill the cell $(i, j)$ with the number $x$.

Not a Little Blue Fish wants you to perform a sequence of operations such that the number $X$ is filled into a cell for the first time at the very last operation. Additionally, Not a Little Blue Fish requires the total number of operations $Q$ to be exactly within the range $[L, R]$. You are asked to construct a possible sequence of operations or report that no such solution exists.

Input

The input consists of a single line containing five integers $N, M, X, L, R$.

Output

If no such solution exists, output a single integer -1.

Otherwise, output the first line containing an integer $Q$ ($L \le Q \le R$), representing the number of operations.

The next $Q$ lines each contain two integers $(i, j)$, describing each operation in order.

Examples

Input 1

7 10 7 10 100

Output 1

43
1 1
2 2
3 3
4 4
5 5
6 6
7 7
1 2
2 3
3 4
4 5
5 6
6 7
7 1
1 3
2 4
3 5
4 6
5 7
6 1
7 2
1 4
2 5
3 6
4 7
5 1
6 2
7 3
1 5
2 6
3 7
4 1
5 2
6 3
7 4
1 6
2 7
3 1
4 2
5 3
6 4
7 5
1 7

Subtasks

For all data, $1 \leq N, M \leq 500$, $1 \leq L \leq R \leq 10^9$, $1 \leq X \leq 10^9$.

Subtask 1 (6 points)

$N \leq 20$

$M \leq 20$

Subtask 2 (6 points)

$N \leq 2$

Subtask 3 (14 points)

$N \leq 5$

Subtask 4 (5 points)

$L = 1, R = 10^9$

Subtask 5 (23 points)

$L = 1$

Subtask 6 (25 points)

$N \neq M$

Subtask 7 (21 points)

No additional constraints.