7468: Game on a Circle

There are nstones on a circle, numbered from 1to nin the clockwise direction such that the next of the i-th stone is the (i+1)-th one (i=1,2,…,n−1)and the next of the n-th stone is the first one.
At the beginning of this game, all the stones exist. You will start from the first stone, and then repeatedly do the following operation until all the stones have been erased:
    1. erase the current stone with probability p, and
    2. move to the next stone that hasn't been erased in the clockwise direction.
Now your task is, for i=1,2,…,n, to calculate the probability that the i-th earliest erased stone is the c-th one.
Due to the precision issue, you are asked to report the probabilities in modulo 998244353(223×7×17+1, a prime). For example, if the irreducible fraction of some output value is xy, then you are asked to output the minimum possible non-negative integer zsuch that x≡yz(mod998244353).

There are several test cases.
The first line contains an integer T(1≤T≤100), denoting the number of test cases. Then follow all the test cases.
For each test case, the only line contains four integers n, a, band c(1≤c≤n≤106,0<a<b<998244353), representing that the number of stones is n, the probability pis aband the special stone is the c-th one.
It is guaranteed that the sum of nin all test cases is no larger than 106.
It is also guaranteed that (1−p)i≢1(mod998244353)for i=1,2,…,nin each test case.

For each test case, output nlines, where the i-th line contains an integer, denoting the probability, in modulo 998244353, that the i-th earliest erased stone is the c-th one.