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; } string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; } 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 = cast(uint)(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 bAdd(T)(T[] bit, int pos, T val) in { assert(0 <= pos && pos < bit.length, "bAdd: 0 <= pos < |bit| must hold"); } do { for (int x = pos; x < bit.length; x |= x + 1) { bit[x] += val; } } // sum of [0, pos) T bSum(T)(T[] bit, int pos) in { assert(0 <= pos && pos <= bit.length, "bSum: 0 <= pos <= |bit| must hold"); } do { T ret = 0; for (int x = pos - 1; x >= 0; x = (x & (x + 1)) - 1) { ret += bit[x]; } return ret; } // floor(a / m) // m > 0 long floor(long a, long m) { return a / m - ((a % m < 0) ? 1 : 0); } // ceil(a / m) // m > 0 long ceil(long a, long m) { return a / m + ((a % m > 0) ? 1 : 0); } // sum{ floor((a x + b) / m) | l <= x <= r } // m > 0 long sumFloors(long m, long a, long b, long l, long r) in { assert(m > 0, "sumFloors: m > 0 must hold"); } do { long sum; for (; l <= r; ) { const q = floor(a, m); const aa = a - q * m; const ll = floor(aa * l + b, m) + 1; const rr = floor(aa * r + b, m); sum += q * ((r + 1) * r / 2 - l * (l - 1) / 2) + r * rr - (l - 1) * (ll - 1) + (rr - ll + 1); a = m; m = aa; l = -rr; r = -ll; } return sum; } void main() { try { for (; ; ) { const N = readInt; const M = readInt; auto D = new int[N]; foreach (i; 0 .. N) { D[i] = readInt; } Mint all = 1; auto ws = new Mint[N]; foreach (i; 0 .. N) { const q = M / D[i]; all *= q; ws[i] = Mint(q).inv; } const sqrtM = cast(int)(sqrt(cast(real)(M))); Mint ans; // small, * { auto fs = new Mint[sqrtM + 1]; foreach_reverse (i; 0 .. N) { if (D[i] <= sqrtM) { ans += ws[i] * fs[D[i]]; } foreach (d; 1 .. sqrtM + 1) { // \sum[1<=x<=M/d] floor((d x - 1) / D[i]) fs[d] += ws[i] * sumFloors(D[i], d, -1, 1, M / d); } } } // large, small { auto fs = new Mint[sqrtM + 1]; foreach (i; 0 .. N) { if (D[i] <= sqrtM) { ans += ws[i] * fs[D[i]]; } if (D[i] > sqrtM) { foreach (d; 1 .. sqrtM + 1) { // \sum[1<=x<=M/d] (floor(M / D[i]) - floor((d x) / D[i])) fs[d] += ws[i] * (Mint(M / d) * Mint(M / D[i]) - sumFloors(D[i], d, 0, 1, M / d)); } } } } // large, large { auto bit = new Mint[M + 1]; foreach_reverse (i; 0 .. N) { if (D[i] > sqrtM) { for (int a = D[i]; a <= M; a += D[i]) { ans += ws[i] * bit.bSum(a); } } if (D[i] > sqrtM) { for (int a = D[i]; a <= M; a += D[i]) { bit.bAdd(a, ws[i]); } } } } ans *= all; writeln(ans); debug { Mint brt; foreach (i; 0 .. N) for (int a = D[i]; a <= M; a += D[i]) { foreach (j; i + 1 .. N) { brt += ws[i] * ws[j] * ((a - 1) / D[j]); } } brt *= all; writeln("brt = ", brt); } } } catch (EOFException e) { } }