public static void Solve()
{
var(N, Q) = Scanner.Scan <int, int>();
S Operation(S a, S b) => new S(a.X * b.W + b.X, a.W * b.W);
var idData = new S(0, 1);
var inv9 = ModuloInteger.Inverse(9);
S Mapping(int f, S x) => f == 0 ? x : new S((x.W - 1) * inv9 * f, x.W);
int Composition(int f, int g) => f == 0 ? g : f;
var idInt = 0;
var lst = new LazySegmentTree <S, int>(N, Operation, idData, Mapping, Composition, idInt);
for (var i = 0; i < N; i++)
{
lst.Set(i, new S(1, 10));
}
for (var i = 0; i < Q; i++)
{
var(L, R, D) = Scanner.Scan <int, int, int>();
lst.Apply(L - 1, R, D);
Console.WriteLine(lst.QueryToAll().X);
}
}
private static void Initialize()
{
if (_sumE != null && _sumIe != null)
{
return;
}
var m = ModuloInteger.Modulo;
_primitiveRoot = PrimitiveRoot(m);
_sumE = new ModuloInteger[30];
_sumIe = new ModuloInteger[30];
var es = new ModuloInteger[30];
var ies = new ModuloInteger[30];
var count2 = BitScanForward(m - 1);
var e = new ModuloInteger(_primitiveRoot).Power((m - 1) >> count2);
var ie = e.Inverse();
for (var i = count2; i >= 2; i--)
{
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
ModuloInteger now = 1;
ModuloInteger inow = 1;
for (var i = 0; i < count2 - 2; i++)
{
_sumE[i] = es[i] * now;
_sumIe[i] = ies[i] * inow;
now *= ies[i];
inow *= es[i];
}
}
public static void Solve()
{
var(N, K) = Scanner.Scan <int, int>();
var A = Scanner.ScanEnumerable <int>().Select(x => (ModuloInteger)x).ToArray();
var sum = new ModuloInteger[K + 1];
for (var i = 0; i < N; i++)
{
ModuloInteger x = 1;
for (var j = 0; j <= K; j++)
{
sum[j] += x;
x *= A[i];
}
}
var i2 = ModuloInteger.Inverse(2);
for (var i = 1; i <= K; i++)
{
ModuloInteger answer = 0;
for (var j = 0; j <= i; j++)
{
answer += EnumerationModulo.Combination(i, j) * (sum[j] * sum[i - j] - sum[i]);
}
answer *= i2;
Console.WriteLine(answer);
}
}
public void Inverse998244353Test()
{
ModuloInteger.Modulo = 998244353;
for (var i = 1; i < 100000; i++)
{
var x = ModuloInteger.Inverse(i);
var y = new ModuloInteger(i).Inverse();
Assert.That(x.Value, Is.GreaterThanOrEqualTo(0));
Assert.That(x.Value, Is.LessThanOrEqualTo(998244353 - 1));
Assert.That(x.Value * i % 998244353, Is.EqualTo(1));
Assert.That(x, Is.EqualTo(y));
}
}
public void InverseTest([Values(11, 12, 1000000007, 1000000008)] int n)
{
ModuloInteger.Modulo = n;
for (var i = 1; i < Math.Min(n, 100000); i++)
{
if (GreatestCommonDivisor(i, n) != 1)
{
continue;
}
var x = ModuloInteger.Inverse(i);
var y = new ModuloInteger(i).Inverse();
Assert.That(x * i % n, Is.EqualTo(1));
Assert.That(x, Is.EqualTo(y));
}
}
public void Modulo1Test()
{
ModuloInteger.Modulo = 1;
for (var i = 0; i < 100; i++)
{
for (var j = 0; j < 100; j++)
{
Assert.That((i * (ModuloInteger)j).Value, Is.Zero);
}
}
ModuloInteger l = 1234;
ModuloInteger r = 5678;
Assert.That((l + r).Value, Is.Zero);
Assert.That((l - r).Value, Is.Zero);
Assert.That((l * r).Value, Is.Zero);
Assert.That(l.Power(r.Value).Value, Is.Zero);
Assert.That(l.Inverse().Value, Is.Zero);
}
