P6202 [USACO07CHN] Summing Sums G

$N$ cows ($1 \leq N \leq 5 \times 10^4$) have just learned a lot about cryptography. At last, they created a cow-only encryption method. Because they lack experience, their encryption method is very simple. The $i$-th cow holds the $i$-th digit of the code, which is initially $C_i$ ($0 \leq C_i \lt 9 \times 10^7$). During encryption, the $i$-th cow computes the sum of the numbers of all other cows, and takes this sum modulo $98\,765\,431$. After all cows finish computing, each cow replaces her original number with the number she computed. That is, $$ C_{i}'=(\sum_{k=1}^NC_k-C_i) \bmod 98\,765\,431 $$ In this way, they complete one encryption. In November, the cows told this encryption method to Carmen the moose. After thinking for a while, Carmen said: "Your algorithm is still very primitive. To achieve an encryption effect, you need to repeat this encryption process $T$ times ($1 \leq T \leq 1\,414\,213\,562$)." The cows are lazy, so they gave this task to you.

The first line contains two integers $N, T$. The next $N$ lines each contain one integer. The $i$-th line contains $C_i$.

Output $N$ lines. The $i$-th line contains one integer, representing $C_i$ after $T$ encryptions.

After each encryption, $C_i$ is as follows: | Number of times | $C_1$ | $C_2$ | $C_3$ | | ---- | ----- | ----- | ----- | | 0 | 1 | 0 | 4 | | 1 | 4 | 5 | 1 | | 2 | 6 | 5 | 9 | | 3 | 14 | 15 | 11 | | 4 | 26 | 25 | 29 | Translated by ChatGPT 5