結果

問題 No.2127 Mod, Sum, Sum, Mod
ユーザー 👑 hos.lyric
提出日時 2022-11-18 22:17:47
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 4,748 bytes
コンパイル時間 1,791 ms
コンパイル使用メモリ 155,732 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-06-22 16:44:15
合計ジャッジ時間 2,734 ms
ジャッジサーバーID
(参考情報)
judge1 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

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 = 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;
// floor(n/x) = k
// <=> k <= n/x < k+1
// <=> n/(k+1) < x <= n/k
// <=> floor(n/(k+1)) < x <= floor(n/k)
void doFloors(alias fun, T)(const(T) n) {
assert(n >= 1);
for (T a = 0, b; a < n; a = b) {
const k = n / (a + 1);
b = n / k;
// (a, b]: k
fun(a, b, k);
}
}
void main() {
try {
for (; ; ) {
const N = readLong + 1;
const M = readLong;
Mint ans;
doFloors!((long a, long b, long k) {
chmax(a, 0);
chmin(b, M);
if (a < b) {
debug {
if (N <= 100) {
writefln("(%s, %s]: %s", a, b, k);
}
}
// Sum[Sum[r, {r, 0, j - 1}], {j, 1, m}]
Mint calc0(long m) {
return Mint(m - 1) * Mint(m) * Mint(m + 1) / 6;
}
// Sum[Sum[r, {r, 0, N - k j - 1}], {j, 1, m}]
Mint calc1(long m) {
const Mint N_ = N;
const Mint k_ = k;
const Mint m_ = m;
return (3*k_*m_ + k_*k_*m_ + 3*k_*m_*m_ + 3*k_*k_*m_*m_ + 2*k_*k_*m_*m_*m_ - 6*m_*N_ - 6*k_*m_*N_ - 6*k_*m_*m_*N_ + 6*m_*N_*N_) / 12;
}
ans += Mint(k) * (calc0(b) - calc0(a));
ans += (calc1(b) - calc1(a));
}
})(N);
if (N < M) {
ans += Mint(M - N) * Mint(N * (N - 1) / 2);
}
writeln(ans);
debug {
if (N <= 100 && M <= 100) {
Mint brt;
foreach (i; 1 .. N) foreach (j; 1 .. M + 1) {
brt += i % j;
}
writeln("brt = ", brt);
assert(brt == ans);
}
}
}
} catch (EOFException e) {
}
}
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