L. Dream Team
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There is a group of $$$n$$$ undergraduate students at SDU who are interested in participating in the upcoming ICPC competitions. For each student, their strength level is known, denoted by a single integer $$$a_i$$$.

There are also $$$m$$$ similar graduate students at the university who are interested in the role of coach. For each of them, their strength level is also known, denoted by a single integer $$$b_i$$$.

The SDU administration is interested in how potentially balanced a team can be assembled from their university. To do this, a team of three undergraduate students $$$i$$$, $$$j$$$, and $$$q$$$ ($$$1 \le i \lt j \lt q \le n$$$) must be formed. The strength of the team will be determined by the sum of the individual members of the team, namely — the number $$$a_i + a_j + a_q$$$.

However, the team will not develop fully without a coach. Therefore, it was decided to choose one coach from the graduate students. Let the number of the selected coach be $$$k$$$ $$$(1 \leq k \leq m)$$$. Then the following conditions must also be met:

  1. The coach must be stronger than the team so that he can train them. Therefore, the condition $$$b_k \gt a_i + a_j + a_q$$$ must be met.
  2. The coach should not be too strong compared to the team so that the coach is not bored teaching, and the participants do not find it too difficult to train.

Taking into account the above restrictions, it was decided to form a suitable team so that the difference between the strength of the coach and the strength of the team $$$b_k - (a_i + a_j + a_q)$$$ was minimal. If it is possible to form several suitable teams, any of them can be chosen.

Help assemble the dream team.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 300$$$) — the number of undergraduate and graduate students, respectively.

The second line contains $$$n$$$ integers $$$a_1, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10000$$$) — the strength levels of undergraduate students.

The third line contains $$$m$$$ integers $$$b_1, \ldots, b_m$$$ ($$$1 \leq b_i \leq 10000$$$) — the strength levels of graduate students.

Output

If it is possible to form the dream team, output four integers $$$i, j, q, k$$$ ($$$1 \leq i \lt j \lt q \leq n$$$, $$$1 \leq k \leq m$$$) — the numbers of the team members and the coach.

If it is impossible to assemble the dream team, output a single integer -1.

Examples
Input
3 2
1 2 3
10 8
Output
1 2 3 2
Input
3 2
1 2 3
6 4
Output
-1
Input
5 5
1 2 4 8 16
6 18 23 27 30
Output
2 3 5 3
Note

In the first example, only three undergraduate students can be selected for the team, and the strength of this team will be $$$1+2+3=6$$$. For the role of coach, we can choose a graduate student with a strength of $$$8$$$ or a graduate student with a strength of $$$10$$$, among them it is best to choose a student with a strength of $$$8$$$ to minimize the difference between the strength of the team and the strength of the coach.

In the second example, the strength of the only possible team is $$$6$$$, and it is impossible to choose a coach who would be stronger than this team.