Problem Description

There are $n$ children in a kindergarten. Initially, the $i$-th child has $a_i$ candies. The teacher can perform an unlimited number of operations. In each operation, she chooses one child and gives them $k$ candies.

To prevent children from getting angry and eating other children's candies, the teacher wants all children to have the same number of candies. If the goal can be achieved, output YES and the minimum number of operations. If it cannot be achieved, output NO directly.

Input Format

The first line contains $2$ integers $n, k$, representing the number of children and the number of candies given in each operation.

The second line contains $n$ integers $a_i$, representing the initial number of candies of the $i$-th child.

Output Format

Output YES or NO on the first line. If you output YES, then output $1$ integer on the next line, representing the answer.

6 3
1 1 4 5 1 4

NO

3 2
9 1 5

YES 6

Hint

Constraints

This problem uses bundled testdata.

• Subtask #1 ($20\text{ pts}$): $n, k \le 10^3$, $a_i \le 10^3$.
• Subtask #2 ($30\text{ pts}$): $k = 1$.
• Subtask #3 ($50\text{ pts}$): no special constraints.

For $100\%$ of the testdata, $1 \le n, k \le 10^5$, $0 \le a_i \le 2^{31} - 1$.

Translated by ChatGPT 5