Array Convergence

By Kay Akashi

Time: 1000 ms

Memory: 256000 kB

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Problem Statement

Given an array consisting of $n$ integers $a_{1}$ , …, $a_{n}$ , you can do a following operation to each element only once: choose any integer $x$ $(-k \leq x \leq k)$ and add $x$ to an element.

As a result of performing the operations to all the elements in the array, can you make all the elements equivalent?

Constraints

$1 \leq n \leq 10^{4}$ , $1 \leq k \leq 2 × 10^{4}$ , $-10^{4} \leq a_i \leq 10^{4} (1 \leq i \leq n)$ .

Input

The first line of input contains two integers, $n$ and $k$ . The second line of input contains $n$ integers that form an array $a$ .

Output

Output "Yes" if you can make all the elements of $a$ equivalent. Otherwise, output "No".

Examples

Input

5 2
-1 3 2 2 0

Output

Yes

Explanation

You can create the new array by adding following numbers to each element respectively: $(2, -2, -1, -1, 1)$ . As a result of those operations, the new array consists of $1$ only and the goal is achieved. Hence the answer is "Yes".

Input

4 1
-83 -10 910 23

Output

No

Array Convergence

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