Problem Statement

DHMO got curious about a puzzle game whose ads keep appearing on a social media app, and decided to play it.
The puzzle game is played by moving a player within a grid with $H$ rows and $W$ columns. The cell in the $i$-th row from the top and the $j$-th column from the left is called $(i,j)$. Cells that do not satisfy ($1 \le i \le H$ and $1 \le j \le W$) do not exist.

The player starts at $(1,1)$ with an attack power of $A_{1,1}$.
Every cell other than $(1,1)$ contains an enemy, and the attack power of the enemy at $(i,j)$ is $A_{i,j}$.
The game is cleared by defeating the boss enemy at $(H,W)$.

When the player is at $(i,j)$, the player can move to whichever of $(i+1,j)$ and $(i,j+1)$ exists.
The player then battles the enemy in the destination cell.
If the player's attack power is higher than the enemy's attack power, the player defeats the enemy, and the player's attack power increases by the enemy's attack power.
If the player's attack power is less than or equal to the enemy's, the player loses, and the game is over unless the player continues.

Upon losing, the player may continue only $1$ time. (This requires watching a 30-second ad twice, but DHMO will put up with it.)
When the player loses at $(i,j)$ and continues, the player avoids the battle with the enemy at $(i,j)$ and can resume the game from $(i,j)$.
In this case, the enemy at $(i,j)$ is not considered defeated, and the player's attack power neither increases nor decreases.
Since a continue does not count as a victory, the player cannot continue at $(H,W)$, and this is treated as game over.

The contents of the puzzle game are given as input.
Determine whether the game can be cleared by controlling the player appropriately.

Input

$H$ $W$
$A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,W}$
$A_{2,1}$ $A_{2,2}$ $\ldots$ $A_{2,W}$
$\vdots$
$A_{H,1}$ $A_{H,2}$ $\ldots$ $A_{H,W}$

Constraints

• $ 2 \le H,W \le 500$
• $ 1 \le A_{i,j} \le 10^{9}$
• All inputs are integers.

Output

Print Yes if the game can be cleared, and No otherwise.

Print a newline at the end.

Sample

3 4
10 8 15 50
5 4 40 50
10 1 30 60

Yes

2 5
10 5 50 10 30
10 10 50 50 20

No

2 2
10 2
1 12

No

5 5
3 2 2 5 20
2 8 1 3 10
9 4 20 40 10
8 7 32 22 88
20 13 26 51 100 

Yes