Given positive integers N, K and M, solve the following problem for every integer x between 1 and N (inclusive):
- Find the number, modulo M, of non-empty multisets containing between 0 and K (inclusive) instances of each of the integers $1, 2, 3 \cdots, N$ such that the average of the elements is x.

-----Constraints-----
- $1 \leq N, K \leq 100$
- $10^8 \leq M \leq 10^9 + 9$
- M is prime.
- All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N K M

-----Output-----
Use the following format:
c_1
c_2
:
c_N

Here, c_x should be the number, modulo M, of multisets such that the average of the elements is x.

-----Sample Input-----
3 1 998244353

-----Sample Output-----
1
3
1

Consider non-empty multisets containing between 0 and 1 instance(s) of each of the integers between 1 and 3. Among them, there are:
- one multiset such that the average of the elements is k = 1: {1};
- three multisets such that the average of the elements is k = 2: {2}, {1, 3}, {1, 2, 3};
- one multiset such that the average of the elements is k = 3: {3}.

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