The Prince's Path

Challenge created by conioh

Note the clarification below

The Prince of Zakarta has a problem. The princess has been kidnapped by the demon. To save the princess he needs to travel through a path similar to figure below, where each line leads to different cities denoted by circles.

At most cities he faces two paths to two different cities. But in the bottom row, there's only one path forward to the end.

In each city the Prince will either find a devil power or good power. The Prince will initially start with the power of the first city he visits. If he passes the city with devil power d then his power will be reduced by d i.e. P - d. Similarly, if he passes the city with good power g his power will be increased by g i.e. P + g.

If, after the first city, his power ever becomes 0 or less, he will Die. The Prince has all the information needed, but he needs your help to tell him whether he can save the Princess.

Clarification: The Prince can start at any city on the left side, even if it's not greater than 0. He only dies if he hits 0 or below at any point afterwards.

I/O format

The first line of input contains c, the number of test cases. c cases follow, with each case in the following format:

• The first line contains n, the number of cities from with which he can start.
• The next line contains m, the number of cities in each path.
• In each of the next n lines there will be m integers i.e. powers.
• A positive power denotes a good power and a negative power denotes an evil power.

Output a YES or NO for each case:

YES if he can save princess.
NO if he can’t.

Example

Input:

3
4
4 2 3 -12
2 1 4 -10
2 0 5 -9

Output:

YES

Explanation:

He can follow this path (0,0) -> (1,1) - > (2,2) -> (3,2)
So his power at the end = 4 + 1 + 5 - 9 = 1
And at every instance it is greater than 0.

Constraints
There can be up to 100 cases in a challenge. Each case can have up to 200 cities.