Weight of the System of Nested Segments solution codeforces

On the number line there are mm points, ii-th of which has integer coordinate xixi and integer weight wiwi. The coordinates of all points are different, and the points are numbered from 11 to mm.

A sequence of nn segments [l1,r1],[l2,r2],,[ln,rn][l1,r1],[l2,r2],…,[ln,rn] is called system of nested segments if for each pair i,ji,j (1i<jn1≤i<j≤n) the condition li<lj<rj<rili<lj<rj<ri is satisfied. In other words, the second segment is strictly inside the first one, the third segment is strictly inside the second one, and so on.

For a given number nn, find a system of nested segments such that:

• both ends of each segment are one of mm given points;
• the sum of the weights 2n2⋅n of the points used as ends of the segments is minimal.

For example, let m=8m=8. The given points are marked in the picture, their weights are marked in red, their coordinates are marked in blue. Make a system of three nested segments:

• weight of the first segment: 1+1=21+1=2
• weight of the second segment: 10+(1)=910+(−1)=9
• weight of the third segment: 3+(2)=13+(−2)=1
• sum of the weights of all the segments in the system: 2+9+1=122+9+1=12

System of three nested segments
Input

The first line of input data contains an integer tt (1t1041≤t≤104) —the number of input test cases.

An empty line is written before each test case.

The first line of each test case contains two positive integers nn (1n1051≤n≤105) and mm (2nm21052⋅n≤m≤2⋅105).

The next mm lines contain pairs of integers xixi (109xi109−109≤xi≤109) and wiwi (104wi104−104≤wi≤104) — coordinate and weight of point number ii (1im1≤i≤m) respectively. All xixi are different.

It is guaranteed that the sum of mm values over all test cases does not exceed 21052⋅105.

Output Weight of the System of Nested Segments solution codeforces

For each test case, output n+1n+1 lines: in the first of them, output the weight of the composed system, and in the next nn lines output exactly two numbers  — the numbers of the points which are the boundaries of the segment with the number ii (1in1≤i≤n). The order in which you output the ends of the segment is not important — you can output the number of the left point first and then the number of the right point, or the other way around.

If there are several ways to make a system of nested segments with minimal weight, output any of them.

Example

input

Copy
3

3 8
0 10
-2 1
4 10
11 20
7 -1
9 1
2 3
5 -2

3 6
-1 2
1 3
3 -1
2 4
4 0
8 2

2 5
5 -1
3 -2
1 0
-2 0
-5 -3


output

Copy
12
2 6
5 1
7 8

10
1 6
5 2
3 4

-6
5 1
4 2
Note

The first test case coincides with the example from the condition. It can be shown that the weight of the composed system is minimal.

The second test case has only 66 points, so you need to use each of them to compose 33 segments.