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문제

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.

입력

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 $A_{i,1}$, $A_{i,2}$, $\ldots$, $A_{i,M}$ ($-10^5 \le A_{i,j} \le 10^5$).

출력

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

예제 입력 1

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

예제 출력 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 $S$.

예제 입력 2

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

예제 출력 2

Yes

예제 입력 3

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

예제 출력 3

No

예제 입력 4

2 2 3 100
0 0
0 0

예제 출력 4

Yes