Author:  N. Grebenyuk  Time limit:  2 sec  
Input file:  Standard input  Memory limit:  256 Mb  
Output file:  Standard output 
Aleksey lost his favourite array a! He remembers that the array consisted of n nonnegative 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} + a_{1})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 nonnegative integers that are not greater than 10^{4}.
The first line contains three integers n, k, sum.
The next line contains n nonnegative integers b_{i}.
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.
2 ≤ n, k ≤ 10^{4}
0 ≤ sum ≤ 10^{9}
0 ≤ a_{i} ≤ 10^{4}
0 ≤ b_{i} < k
No.  Standard input  Standard output 

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