public override void Solve(IOManager io)
{
var n = io.ReadInt();
var k = io.ReadInt();
var pows = new ModInt[k + 1][];
pows[0] = new ModInt[n];
pows[0].Fill(ModInt.One);
pows[1] = new ModInt[n];
for (int i = 0; i < pows[1].Length; i++)
{
pows[1][i] = ModInt.Raw(io.ReadInt());
}
var combination = new ModCombination <Mod998244353>(300);
for (int p = 2; p < pows.Length; p++)
{
pows[p] = new ModInt[n];
for (int i = 0; i < pows[p].Length; i++)
{
pows[p][i] = pows[p - 1][i] * pows[1][i];
}
}
var sums = new ModInt[k + 1];
for (int p = 0; p < pows.Length; p++)
{
var sum = ModInt.Zero;
for (int i = 0; i < pows[p].Length; i++)
{
sum += pows[p][i];
}
sums[p] = sum;
}
var invTwo = ModInt.Raw(2).Inverse();
for (int x = 1; x < pows.Length; x++)
{
var result = ModInt.Zero;
for (int r = 0; r <= x; r++)
{
result += combination.Combination(x, r) * sums[r] * sums[x - r];
}
var sub = ModInt.Raw(2).Pow(x) * sums[x];
result -= sub;
result *= invTwo;
io.WriteLine(result);
}
}
public void Test組み合わせ(long m, long n, long expected)
{
var c = new ModCombination();
Assert.Equal(expected, c.Combination(m, n));
}
public void CombinationTest(int n, int r, int expected)
{
var fact = _combination.Combination(n, r);
Assert.Equal(expected, fact.Value);
}