public void Solve_1()
{
var crt1 = new CRT(3, 5);
var crt2 = new CRT(15, 7);
var x1 = crt1.Solve(2, 3);
var x2 = crt2.Solve(x1, 2);
Assert.AreEqual(23, x2);
}
public void Solve_2()
{
var expected = 1_000000000_000000000;
var p1 = 998244353;
var p2 = 1107296257;
var crt = new CRT(p1, p2);
var actual = crt.Solve(expected % p1, expected % p2);
Assert.AreEqual(expected, actual);
}
static void Main()
{
var n = int.Parse(Console.ReadLine());
var a = new long[n + 1];
var b = new long[n + 1];
for (int i = 1; i <= n; i++)
{
var v = Read();
a[i] = v[0];
b[i] = v[1];
}
var ab1 = new FNTT302(1 << 20, p1, g1).Convolution(a, b);
var ab2 = new FNTT302(1 << 20, p2, g2).Convolution(a, b);
var crt = new CRT(p1, p2);
var ab = ab1.Zip(ab2, (x, y) => crt.Solve(x, y)).ToArray();
Console.WriteLine(string.Join("\n", ab[1..]));
static object Solve()
{
var n = int.Parse(Console.ReadLine());
var a = ReadL();
// g^{p-1} == 1
var pg = new long[p - 1];
var pgMap = new long[p];
pg[0] = 1;
for (int i = 1; i < pg.Length; i++)
{
pg[i] = pg[i - 1] * g % p;
pgMap[pg[i]] = i;
}
var r = 0L;
var c = new long[p - 1];
foreach (var x in a)
{
if (x == 0)
{
continue;
}
c[pgMap[x]]++;
r -= x * x % p;
}
var c1 = new FNTT302(1 << 20, p1, g1).Convolution(c, c);
var c2 = new FNTT302(1 << 20, p2, g2).Convolution(c, c);
var crt = new CRT(p1, p2);
var conv = c1.Zip(c2, (x, y) => crt.Solve(x, y)).ToArray();
for (int i = 0; i < conv.Length; i++)
{
r += conv[i] * pg[i % (p - 1)];
}
return(r / 2);
}
public void Convolution()
{
const long p1 = 998244353, g1 = 3;
const long p2 = 1107296257, g2 = 10;
var fntt1 = new FNTT202(8, p1, g1);
var fntt2 = new FNTT202(8, p2, g2);
var a = new long[] { 1000000, 1000000, 1000000 };
var b = new long[] { 1000000, 1000000, 1000000, 1000000 };
var c1 = fntt1.Convolution(a, b);
var c2 = fntt2.Convolution(a, b);
var crt = new CRT(p1, p2);
var c = c1.Zip(c2, (x, y) => crt.Solve(x, y)).ToArray();
var expected = new long[] { 1000000000000, 2000000000000, 3000000000000, 3000000000000, 2000000000000, 1000000000000, 0, 0 };
CollectionAssert.AreEqual(expected, c);
}