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; // Pretty print (smaller abs) int[] pretty(uint M)(ModInt!M[] as) { return (cast(const(ModInt!M[]))(as)).pretty; } int[] pretty(uint M)(const(ModInt!M[]) as) { import std.algorithm : map; import std.array : array; return as.map!(a => (a.x < M - a.x) ? cast(int)(a.x) : -cast(int)(M - a.x)).array; } // Berlekamp-Massey // F: field // \sum_{j=1}^0 cs[j] as[i - j] = 0 (d <= i < |as|), cs[0] = 1 F[] findLinearRecurrence(F)(inout(F)[] as) { import std.algorithm : min; const n = cast(int)(as.length); int d, m; auto cs = new F[n + 1], bs = new F[n + 1]; cs[0] = bs[0] = 1; F invBef = 1; foreach (i; 0 .. n) { ++m; F dif = as[i]; foreach (j; 1 .. d + 1) dif += cs[j] * as[i - j]; if (dif.x != 0) { auto csDup = cs.dup; const r = dif * invBef; foreach (j; m .. n) cs[j] -= r * bs[j - m]; if (2 * d <= i) { d = i + 1 - d; m = 0; bs = csDup; invBef = dif.inv; } } } return cs[0 .. d + 1]; } ModInt!M[] findLinearRecurrence(uint M)(long[] as) { import std.algorithm : map; import std.array : array; return findLinearRecurrence(as.map!(a => ModInt!M(a)).array); } // x^e mod rev(cs) Mint[] powerRev(const(Mint[]) cs, long e) { assert(!cs.empty); assert(cs[0].x == 1); const d = cast(int)(cs.length) - 1; if (d == 0) { return []; } else if (d == 1) { return [cs[0]^^e]; } Mint[] mul(Mint[] fs, Mint[] gs) { auto hs = new Mint[d + d - 1]; foreach (i; 0 .. d) foreach (j; 0 .. d) { hs[i + j] += fs[i] * gs[j]; } foreach_reverse (i; d .. d + d - 1) { foreach (j; 1 .. d + 1) { hs[i - j] -= cs[j] * hs[i]; } } hs.length = d; return hs; } auto xs = new Mint[d]; auto ys = new Mint[d]; xs[1] = 1; ys[0] = 1; for (; ; xs = mul(xs, xs)) { if (e & 1) ys = mul(ys, xs); if (!(e >>= 1)) break; } return ys; } Mint linearRecurrenceAt(const(Mint[]) as, const(Mint[]) cs, long e) { assert(!cs.empty); assert(cs[0].x == 1); const d = cast(int)(cs.length) - 1; assert(as.length >= d); const fs = powerRev(cs, e); Mint ans; foreach (i; 0 .. d) { ans += as[i] * fs[i]; } return ans; } enum E = 64; enum LIM = 2 * E + 5; void main() { try { for (; ; ) { const N = readLong; const M = readLong; auto freq1 = new Mint[][](E, 2); auto freq2 = new Mint[][][][](E, E, 2, 2); /* foreach (e; 0 .. E) { foreach (x; 0 .. M) { freq1[e][x >> e & 1] += 1; } } foreach (e; 0 .. E) foreach (f; 0 .. E) { foreach (x; 0 .. M) { freq2[e][f][x >> e & 1][x >> f & 1] += 1; } } */ for (long m = M; m; ) { const e0 = bsf(m); m &= m - 1; const Mint all = (1L << e0); const Mint half = all / 2; const Mint quar = all / 4; foreach (e; 0 .. e0) { foreach (a; 0 .. 2) { freq1[e][a] += half; } } foreach (e; e0 .. E) { freq1[e][m >> e & 1] += all; } foreach (e; 0 .. e0) foreach (f; 0 .. e0) if (e != f) { foreach (a; 0 .. 2) foreach (b; 0 .. 2) { freq2[e][f][a][b] += quar; } } foreach (e; 0 .. e0) foreach (f; e0 .. E) { foreach (a; 0 .. 2) { freq2[e][f][a][m >> f & 1] += half; freq2[f][e][m >> f & 1][a] += half; } } foreach (e; e0 .. E) foreach (f; e0 .. E) { freq2[e][f][m >> e & 1][m >> f & 1] += all; } } auto dp = new Mint[][][](LIM, E, 2); foreach (e; 0 .. E) foreach (a; 0 .. 2) { dp[2][e][a] += freq1[e][a ^ 1] * Mint(1L << e); } foreach (i; 2 .. LIM - 1) { foreach (e; 0 .. E) foreach (a; 0 .. 2) { foreach (ee; 0 .. E) { if (e != ee) { foreach (aa; 0 .. 2) { dp[i + 1][ee][aa] += dp[i][e][a] * freq2[e][ee][a][aa ^ 1] * Mint(1L << ee); } } else { dp[i + 1][ee][a ^ 1] += dp[i][e][a] * freq1[e][a] * Mint(1L << ee); } } } } auto as = new Mint[LIM]; foreach (i; 0 .. LIM) { foreach (e; 0 .. E) foreach (a; 0 .. 2) { as[i] += dp[i][e][a] * freq1[e][a]; } } const cs = findLinearRecurrence(as); debug { writeln("as = ", as); writeln("cs = ", cs); } const ans = linearRecurrenceAt(as, cs, N); writeln(ans); } } catch (EOFException e) { } }