Problem Statement

One day, Iroha-chan was telling Meguru-chan about her hometown.
In Iroha-chan's hometown, several villages were connected by several directed waterways.
The villages were numbered 0, 1, 2, ... in order. Among them, village 0 and village 1 were special villages that served as water sources.
When water is released from village 0 or village 1, it reaches every village reachable by following the waterways in their directions.
A single waterway never goes from a village $x$ to the same village $x$, but water may return to its original village by passing through several waterways.
Also, water may flow into village 0 or village 1 from other villages.
According to Iroha-chan, her hometown satisfied all of the following conditions.

• The hometown had 2 or more villages.
• Every village received water from village 0 or village 1.
• When water was released from village 0, it reached $A$ villages, including village 0.
• When water was released from village 1, it reached $B$ villages, including village 1.
• The number of villages that received water from both village 0 and village 1 was $C$. (Here, $C \leq \min(A, B)$ holds.)
• There were at most $D$ waterways.

Input

$A$ $B$ $C$ $D$

The input consists of one line, in which the values $A, B, C, D$ from the statement are given separated by spaces.
$A, B, C, D$ satisfy the following conditions.

• $A, B, C, D$ are integers
• $1 \leq A \leq 10^4$
• $1 \leq B \leq 10^4$
• $0 \leq C \leq \min(A, B)$
• $0 \leq D \leq 10^5$

Output

Output as follows.

• If no combination satisfying the problem's conditions exists, print -1, followed by a newline.
  In this case, the output is only one line.
• Otherwise, the output is as follows.

  $N$ $M$
  $a_1$ $b_1$
  $a_2$ $b_2$
  $\dots$
  $a_M$ $b_M$
  

  • On the first line, print the number of villages $N$ and the number of waterways $M$.
  • On each of lines 2 through $M + 1$, when a waterway exists in the direction from village $a_i$ to village $b_i$, print $a_i$ and $b_i$ separated by a space.
  • However, you must not print the same waterway more than once. Also, $0 \leq a_i, b_i < N, a_i \neq b_i$ must be satisfied.
  • Furthermore, all output values must fit in a signed 64-bit integer type, and the entire output must fit within 20MB.
  • Print a newline at the end.

Sample

6 4 2 12

8 10
0 2
0 4
1 2
1 7
2 3
4 2
4 3
4 5
4 6
7 3

5 3 3 5

5 4
0 1
0 2
1 3
1 4

1 4 0 3

5 3
1 2
1 3
1 4

9 8 5 10

-1