import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = x_ % M; } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; void main() { try { for (; ; ) { const N = readInt(); const Q = readInt(); Mint[4] anss; // 0: 1 anss[0] = Q; anss[0] *= Mint(-1 + N) * Mint(2 + N) / 24; // 1: (2 i + 2 i^2 - n - 2 i n + n^2) foreach (i; 0 .. N) { Mint q = 2 * i + 2 * Mint(i)^^2 - N - 2 * Mint(i) * Mint(N) + Mint(N)^^2; q /= Mint(N) * Mint(N + 1); Mint tmp = (q.x == 1) ? Mint(Q) : ((1 - q^^Q) / (1 - q)); tmp *= Mint(1 + i) * Mint(i - N) * Mint(1 + i - N) / (2 * Mint(N) * Mint(1 + N)); anss[1] += tmp; } // 2: (2 j + 2 j^2 - n - 2 j n + n^2) foreach (j; 0 .. N) { Mint q = 2 * j + 2 * Mint(j)^^2 - N - 2 * Mint(j) * Mint(N) + Mint(N)^^2; q /= Mint(N) * Mint(N + 1); Mint tmp = (q.x == 1) ? Mint(Q) : ((1 - q^^Q) / (1 - q)); tmp *= -Mint(j) * Mint(1 + j) * Mint(j - N) / (2 * Mint(N) * Mint(1 + N)); anss[2] += tmp; } // 3: (2 (j - i)^2 + (1 + n) (2 i - 2 j + n)) foreach (d; 1 .. N) { Mint q = 2 * Mint(d)^^2 + Mint(1 + N) * Mint(-2 * d + N); q /= Mint(N) * Mint(N + 1); Mint tmp = (q.x == 1) ? Mint(Q) : ((1 - q^^Q) / (1 - q)); tmp *= Mint(-d + N) * Mint(1 - d + N) * Mint(2 - d + N) / (6 * Mint(N) * Mint(1 + N)); anss[3] += tmp; } foreach (s; 0 .. 4) { anss[s] /= 4; } Mint ans = (anss[0] + anss[1] - anss[2] - anss[3]); ans *= (Mint(N) * Mint(N + 1))^^Q; debug { writeln("anss = ", anss); } writeln(ans); debug { if (N <= 10) { Mint[4] brts; foreach (i; 0 .. N) foreach (j; i + 1 .. N) { Mint[4] ps, qs; ps[1] = Mint(i + 1) * Mint(j - i); ps[3] = Mint(i + 1) * Mint(N - j); ps[2] = Mint(j - i) * Mint(N - j); ps[0] = Mint(N) * Mint(N + 1) - ps[1] - ps[2] - ps[3]; foreach (s; 0 .. 4) { ps[s] /= Mint(N) * Mint(N + 1); } foreach (s; 0 .. 4) foreach (t; 0 .. 4) { qs[s] += (-1)^^popcnt(s & t) * ps[t]; } foreach (s; 0 .. 4) { qs[s] = (qs[s].x == 1) ? Mint(Q) : ((1 - qs[s]^^Q) / (1 - qs[s])); } foreach (s; 0 .. 4) { brts[s] += ps[3] * qs[s] / 4; } } Mint brt = (brts[0] + brts[1] - brts[2] - brts[3]); brt *= (Mint(N) * Mint(N + 1))^^Q; writeln("brts = ", brts, ", brt = ", brt); } } } } catch (EOFException e) { } }