Problem E7. Guess the array ≡

Statement

Aleksey lost his favourite array a! He remembers that the array consisted of n non-negative integers, and its sum was equal to sum.

Recently Aleksey found his calculations on this array. His calculations consist of n numbers b_i such that

b_i = (a_i + a_i + 1)mod k for 1 ≤ i < n

b_n = (a_n + a₁)mod k (a_i — favourite array numbers)

Help Aleksey to find any correct favourite array a corresponding to the array b, or tell him that he has made a mistake, and there is no such array. Notice, that all elements of source array are non-negative integers that are not greater than 10⁴.

Input format

The first line contains three integers n, k, sum.

The next line contains n non-negative integers b_i.

Output format

If the answer exists, print "YES" in the first line and n space separated numbers of array a in the second line. If there are multiple answers, print any of them.

Print "NO" if there is no such array.

Constraints

2 ≤ n, k ≤ 10⁴

0 ≤ sum ≤ 10⁹

0 ≤ a_i ≤ 10⁴

0 ≤ b_i < k

Sample tests

6 4 21
3 1 3 1 3 3

YES
1 2 3 4 5 6

2 7 32
4 4

YES
11 21

6 4 21
1 3 2 1 3 2

NO