結果
| 問題 | No.1781 LCM |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2021-12-10 00:16:55 |
| 言語 | D (dmd 2.106.1) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 9,407 bytes |
| コンパイル時間 | 1,510 ms |
| コンパイル使用メモリ | 159,928 KB |
| 実行使用メモリ | 19,052 KB |
| 最終ジャッジ日時 | 2024-06-22 13:35:35 |
| 合計ジャッジ時間 | 8,347 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1 ms
6,812 KB |
| testcase_01 | AC | 5 ms
6,940 KB |
| testcase_02 | AC | 5 ms
6,944 KB |
| testcase_03 | AC | 5 ms
6,940 KB |
| testcase_04 | AC | 5 ms
6,944 KB |
| testcase_05 | AC | 4 ms
6,944 KB |
| testcase_06 | AC | 5 ms
6,944 KB |
| testcase_07 | AC | 1 ms
6,940 KB |
| testcase_08 | AC | 1 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | AC | 3 ms
6,948 KB |
| testcase_11 | AC | 1 ms
6,940 KB |
| testcase_12 | AC | 1 ms
6,940 KB |
| testcase_13 | AC | 2 ms
6,940 KB |
| testcase_14 | AC | 2 ms
6,940 KB |
| testcase_15 | AC | 2 ms
6,944 KB |
| testcase_16 | AC | 1 ms
6,940 KB |
| testcase_17 | AC | 2 ms
6,944 KB |
| testcase_18 | AC | 1 ms
6,940 KB |
| testcase_19 | AC | 1 ms
6,944 KB |
| testcase_20 | AC | 1 ms
6,944 KB |
| testcase_21 | TLE | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
ソースコード
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;
// floor(sqrt(a))
long floorSqrt(long a) {
import core.bitop : bsr;
import std.algorithm : min;
long b = a, x = 0, y = 0;
for (int e = bsr(a) & ~1; e >= 0; e -= 2) {
x <<= 1;
y <<= 1;
if (b >= (y | 1) << e) {
b -= (y | 1) << e;
x |= 1;
y += 2;
}
}
return x;
}
// get(floor(N / l)) = \sum_{p<=floor(N/l)} p^K
// O(N^(3/4) / log N) time, O(N^(1/2)) space
class PrimeSum(T, int K) {
long N, sqrtN;
bool[] isPrime;
T[] small, large;
this(long N) {
assert(N >= 1, "PrimeSum: N >= 1 must hold");
this.N = N;
sqrtN = floorSqrt(N);
isPrime = new bool[sqrtN + 1];
small = new T[sqrtN + 1];
large = new T[sqrtN + 1];
isPrime[2 .. $] = true;
T powerSum(long n) {
static if (K == 0) {
return T(n);
} else static if (K == 1) {
long n0 = n, n1 = n + 1;
((n0 % 2 == 0) ? n0 : n1) /= 2;
return T(n0) * T(n1);
} else static if (K == 2) {
long n0 = n, n1 = n + 1, n2 = 2 * n + 1;
((n0 % 2 == 0) ? n0 : n1) /= 2;
((n0 % 3 == 0) ? n0 : (n1 % 3 == 0) ? n1 : n2) /= 3;
return T(n0) * T(n1) * T(n2);
} else static if (K == 3) {
long n0 = n, n1 = n + 1;
((n0 % 2 == 0) ? n0 : n1) /= 2;
return T(n0) * T(n0) * T(n1) * T(n1);
} else {
static assert(false, "PrimeSum: K is out of range");
}
}
foreach (n; 1 .. sqrtN + 1) small[n] = powerSum(n);
foreach (l; 1 .. sqrtN + 1) large[l] = powerSum(N / l);
foreach (p; 2 .. sqrtN + 1) {
if (isPrime[p]) {
for (long n = p^^2; n <= sqrtN; n += p) isPrime[n] = false;
const pk = T(p)^^K, g1 = get(p - 1);
foreach (l; 1 .. sqrtN + 1) {
const n = N / l;
if (n < p^^2) break;
large[l] -= pk * (get(n / p) - g1);
}
foreach_reverse (n; 1 .. sqrtN + 1) {
if (n < p^^2) break;
small[n] -= pk * (get(n / p) - g1);
}
}
}
small[1 .. $] -= T(1);
large[1 .. $] -= T(1);
}
T get(long n) const {
return (n <= sqrtN) ? small[n] : large[N / n];
}
}
// get(floor(N / l)) = \sum_{p<=floor(N/l)} p^K
// O(N^(3/4) / log N) time, O(N^(1/2)) space
// large K; \sum_{i=1}^n i^K = \sum_{j=1}^{K+1} coef[j] n^j
class PrimeSum(T) {
long N, sqrtN;
bool[] isPrime;
T[] small, large;
this(long N, int K, T[] coef) {
assert(N >= 1, "PrimeSum: N >= 1 must hold");
this.N = N;
sqrtN = floorSqrt(N);
isPrime = new bool[sqrtN + 1];
small = new T[sqrtN + 1];
large = new T[sqrtN + 1];
isPrime[2 .. $] = true;
T powerSum(long n) {
T y = 0;
foreach_reverse (k; 1 .. K + 2) (y += coef[k]) *= n;
return y;
}
foreach (n; 1 .. sqrtN + 1) small[n] = powerSum(n);
foreach (l; 1 .. sqrtN + 1) large[l] = powerSum(N / l);
foreach (p; 2 .. sqrtN + 1) {
if (isPrime[p]) {
for (long n = p^^2; n <= sqrtN; n += p) isPrime[n] = false;
const pk = T(p)^^K, g1 = get(p - 1);
foreach (l; 1 .. sqrtN + 1) {
const n = N / l;
if (n < p^^2) break;
large[l] -= pk * (get(n / p) - g1);
}
foreach_reverse (n; 1 .. sqrtN + 1) {
if (n < p^^2) break;
small[n] -= pk * (get(n / p) - g1);
}
}
}
small[1 .. $] -= T(1);
large[1 .. $] -= T(1);
}
T get(long n) const {
return (n <= sqrtN) ? small[n] : large[N / n];
}
}
// get(floor(N / l)) = \sum_{n=1}^{floor(N/l)} f(n)
// O(N^(3/4) / log N) time, O(N^(1/2)) space
// f: multiplicative function, f(p): poly in p
class MultiplicativeSum(T) {
long N, sqrtN;
bool[] isPrime;
T[] smallFP, small, large;
this(long N) {
assert(N >= 1, "PrimeSum: N >= 1 must hold");
this.N = N;
sqrtN = floorSqrt(N);
isPrime = new bool[sqrtN + 1];
smallFP = new T[sqrtN + 1];
small = new T[sqrtN + 1];
large = new T[sqrtN + 1];
isPrime[2 .. $] = true;
foreach (p; 2 .. sqrtN + 1) {
if (isPrime[p]) {
for (long n = p^^2; n <= sqrtN; n += p) isPrime[n] = false;
}
}
}
// prepare \sum_{p<=n} f(p) and \sum_{N^(1/2)<p<=floor(N/l)} f(p)
void add(S)(T coef, S primeSum) {
assert(N == primeSum.N, "MultiplicativeSum: N must agree");
foreach (n; 1 .. sqrtN + 1) smallFP[n] += coef * primeSum.small[n];
foreach (l; 1 .. sqrtN + 1) {
large[l] += coef * (primeSum.large[l] - primeSum.small[sqrtN]);
}
}
// (p, e) -> f(p^e)
void build(T delegate(long, int) f) {
import std.algorithm : max;
small[1 .. $] += T(1);
large[1 .. $] += T(1);
foreach_reverse (p; 2 .. sqrtN + 1) {
if (isPrime[p]) {
// added f(p') for p < p' <= min{n, N^(1/2)}
T getAdded(long n) const {
return (n <= sqrtN) ? (small[n] + smallFP[max(n, p)] - smallFP[p])
: (large[N / n] + smallFP[sqrtN] - smallFP[p]);
}
// p^e, f(p^e)
long[] pes = [1];
T[] fs = [T(1)];
long pe = p;
for (int e = 1; ; ++e) {
pes ~= pe;
fs ~= f(p, e);
if (pe > N / p) break;
pe *= p;
}
const limE = cast(int)(pes.length);
foreach (l; 1 .. sqrtN + 1) {
const n = N / l;
if (n < p^^2) break;
for (int e = 1; e < limE && pes[e] <= n; ++e) {
large[l] += fs[e] * getAdded(n / pes[e]);
}
large[l] -= fs[1];
}
foreach_reverse (n; 1 .. sqrtN + 1) {
if (n < p^^2) break;
for (int e = 1; e < limE && pes[e] <= n; ++e) {
small[n] += fs[e] * getAdded(n / pes[e]);
}
small[n] -= fs[1];
}
}
}
small[] += smallFP[];
large[1 .. $] += smallFP[sqrtN];
}
T get(long n) const {
return (n <= sqrtN) ? small[n] : large[N / n];
}
}
enum E = 40;
void main() {
try {
for (; ; ) {
const N = readLong();
const M = readLong();
auto ms = new MultiplicativeSum!Mint(M);
ms.add(Mint(1 + 1)^^N, new PrimeSum!(Mint, 0)(M));
auto pw = new Mint[E];
foreach (e; 0 .. E) {
pw[e] = Mint(e + 1)^^N;
}
ms.build((p, e) => pw[e]);
const Mint ans = ms.get(M);
writeln(ans);
}
} catch (EOFException e) {
}
}