Background

Original problem link: https://oier.team/problems/J2A.

Problem Description

You are given four positive integers $a, b, c, d$.

Now you have an expression $(a\ \Box\ b)\ \Box\ c$. You need to determine whether it is possible to fill each of the two boxes with one of the three operators $+, -, \times$ (operators may be reused) so that the value of the expression equals $d$.

Input Format

The first line contains four positive integers $a, b, c, d$.

Output Format

If it is possible to make the result equal to $d$, output Yes; otherwise output No.

1 1 1 3

Yes

5 2 9 27

Yes

1 1 4 514

No

Hint

Sample Explanation #1

Because $(1 + 1) + 1 = 3$, you can put $+$ in the first box and $+$ in the second box.

Sample Explanation #2

Because $(5 - 2) \times 9 = 27$, you can put $-$ in the first box and $\times$ in the second box.

Sample Explanation #3

No matter which operators you choose, you cannot make the result of the expression equal to $514$.

Constraints

For all testdata, $1 \le a, b, c \le 10$ and $1 \le d \le 1000$.

Translated by ChatGPT 5