Contest Duration: - (local time) (300 minutes) Back to Home
G - Low Range-Sum Matrix /

Time Limit: 2 sec / Memory Limit: 512 MB

### Problem Statement

You received a card at a banquet. On the card, a matrix of $N$ rows and $M$ columns and two integers $K$ and $S$ are written. All the elements in the matrix are integers, and an integer at the $i$-th row from the top and the $j$-th column from the left is denoted by $A_{i,j}$.

You can select up to $K$ elements from the matrix and invert the sign of the elements. If you can make a matrix such that there is no vertical or horizontal contiguous subsequence whose sum is greater than $S$, you can exchange your card for a prize.

Your task is to determine if you can exchange a given card for a prize.

### Input

The input consists of a single test case of the following form.

$N$ $M$ $K$ $S$ $A_{1,1}$ $A_{1,2}$ $\cdots$ $A_{1,M}$ $\vdots$ $A_{N,1}$ $A_{N,2}$ $\cdots$ $A_{N,M}$

The first line consists of four integers $N$, $M$, $K$, and $S$ ($1 \le N, M \le 10$, $1 \le K \le 5$, $1 \le S \le 10^6$). The following $N$ lines represent the matrix in your card. The $(i+1)$-th line consists of $M$ integers $A_{i,1}$, $A_{i,2}$, $\ldots$, $A_{i,M}$ ($-10^5 \le A_{i,j} \le 10^5$).

### Output

If you can exchange your card for a prize, print Yes. Otherwise, print No.

### Sample Input 1

3 3 2 10
5 3 7
2 6 1
3 4 1


### Output for Sample Input 1

Yes


The sum of a horizontal contiguous subsequence from $A_{1,1}$ to $A_{1,3}$ is $15$. The sum of a vertical contiguous subsequence from $A_{1,2}$ to $A_{3,2}$ is $13$. If you flip the sign of $A_{1,2}$, there is no vertical or horizontal contiguous subsequence whose sum is greater than $S$.

### Sample Input 2

2 3 1 5
4 8 -2
-2 -5 -3


### Output for Sample Input 2

Yes


### Sample Input 3

2 3 1 5
9 8 -2
-2 -5 -3


### Output for Sample Input 3

No


### Sample Input 4

2 2 3 100
0 0
0 0


### Output for Sample Input 4

Yes