public void Ntt_Convolution_Many()
{
var a = Enumerable.Range(3, 1 << 16).Select(x => (long)x).ToArray();
var b = Enumerable.Range(7, 1 << 16).Select(x => (long)x).ToArray();
Ntt.Convolution(a, b);
}
public void Convolution()
{
var a = new long[] { 1, 2, 3, 4 };
var b = new long[] { 5, 6, 7, 8, 9 };
var expected = new long[] { 5, 16, 34, 60, 70, 70, 59, 36 };
CollectionAssert.AreEqual(expected, Dft.Convolution(a, b));
CollectionAssert.AreEqual(expected, Dft0.Convolution(a, b));
CollectionAssert.AreEqual(expected, Ntt.Convolution(a, b));
CollectionAssert.AreEqual(expected, Ntt0.Convolution(a, b));
}
public void Ntt_Fft_Many()
{
var n = 1 << 16;
var a = Enumerable.Range(3, n).Select(x => (long)x).ToArray();
var ntt = new Ntt(n);
var t = ntt.Fft(a);
var r = ntt.Fft(t, true);
CollectionAssert.AreEqual(a, r);
}
// 長さは n 以下で OK。
public static long[] Convolution(long[] a, long[] b)
{
var ntt = new Ntt(a.Length + b.Length - 1);
var fa = ntt.Fft(a);
var fb = ntt.Fft(b);
for (int i = 0; i < ntt.n; ++i)
{
fa[i] = fa[i] * fb[i] % p;
}
return(ntt.Fft(fa, true));
}
static void Main()
{
var(n, k) = Read2();
var a = ReadL();
var p2 = new long[k + 1];
var f = new long[k + 1];
var f_ = new long[k + 1];
p2[0] = f[0] = f_[0] = 1;
for (int x = 1; x <= k; x++)
{
p2[x] = p2[x - 1] * 2 % M;
f[x] = f[x - 1] * x % M;
f_[x] = f_[x - 1] * MInv(x) % M;
}
var pa = Array.ConvertAll(a, _ => 1L);
var s1 = new long[k + 1];
var s2 = new long[k + 1];
s1[0] = n;
for (int x = 1; x <= k; x++)
{
var sum = 0L;
for (int i = 0; i < n; i++)
{
sum += pa[i] = pa[i] * a[i] % M;
}
sum %= M;
s1[x] = sum * f_[x] % M;
s2[x] = sum * p2[x] % M;
}
var conv = Ntt.Convolution(s1, s1);
var half = MInv(2);
for (int x = 1; x <= k; x++)
{
Console.WriteLine(MInt((f[x] * conv[x] % M - s2[x]) * half));
}
}
public void Ntt_Fft()
{
var n = 1 << 4;
var a = Enumerable.Range(3, n).Select(x => (long)x).ToArray();
var t0 = Ntt0.Naive(a);
var r0 = Ntt0.Naive(t0, true);
var t1 = Ntt0.Fft(a);
var r1 = Ntt0.Fft(t1, true);
var ntt = new Ntt(n);
var t2 = ntt.Fft(a);
var r2 = ntt.Fft(t2, true);
CollectionAssert.AreEqual(t0, t1);
CollectionAssert.AreEqual(t0, t2);
CollectionAssert.AreEqual(a, r0);
CollectionAssert.AreEqual(a, r1);
CollectionAssert.AreEqual(a, r2);
}
