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Zero Path

2000ms 262144K

Description:

You are given a grid with $$$n$$$ rows and $$$m$$$ columns. We denote the square on the $$$i$$$-th ($$$1\le i\le n$$$) row and $$$j$$$-th ($$$1\le j\le m$$$) column by $$$(i, j)$$$ and the number there by $$$a_{ij}$$$. All numbers are equal to $$$1$$$ or to $$$-1$$$.

You start from the square $$$(1, 1)$$$ and can move one square down or one square to the right at a time. In the end, you want to end up at the square $$$(n, m)$$$.

Is it possible to move in such a way so that the sum of the values written in all the visited cells (including $$$a_{11}$$$ and $$$a_{nm}$$$) is $$$0$$$?

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 10^4$$$). Description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 1000$$$)  — the size of the grid.

Each of the following $$$n$$$ lines contains $$$m$$$ integers. The $$$j$$$-th integer on the $$$i$$$-th line is $$$a_{ij}$$$ ($$$a_{ij} = 1$$$ or $$$-1$$$)  — the element in the cell $$$(i, j)$$$.

It is guaranteed that the sum of $$$n\cdot m$$$ over all test cases does not exceed $$$10^6$$$.

Output:

For each test case, print "YES" if there exists a path from the top left to the bottom right that adds up to $$$0$$$, and "NO" otherwise. You can output each letter in any case.

Sample Input:

5
1 1
1
1 2
1 -1
1 4
1 -1 1 -1
3 4
1 -1 -1 -1
-1 1 1 -1
1 1 1 -1
3 4
1 -1 1 1
-1 1 -1 1
1 -1 1 1

Sample Output:

NO
YES
YES
YES
NO

Note:

One possible path for the fourth test case is given in the picture in the statement.

Informação

Codeforces

Provedor Codeforces

Código CF1695C

Tags

brute forcedata structuresdpgraphsgreedyshortest paths

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Datas 09/05/2023 10:29:10

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