結果
| 問題 | No.1648 Sum of Powers |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2021-08-13 22:04:17 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
AC
|
| 実行時間 | 22 ms / 2,000 ms |
| コード長 | 6,308 bytes |
| コンパイル時間 | 837 ms |
| コンパイル使用メモリ | 130,432 KB |
| 実行使用メモリ | 9,188 KB |
| 最終ジャッジ日時 | 2024-06-22 12:04:25 |
| 合計ジャッジ時間 | 3,815 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 56 |
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;// !!!old library!!!Int mod(Int)(Int a, Int m) {if ((a %= m) < 0) a += m; return a;}Int gcd(Int)(Int a, Int b) { return (b != 0) ? gcd(b, a % b) : a; }Int lcm(Int)(Int a, Int b) { return a / gcd(a, b) * b; }Int gojo(Int)(Int a, Int b, out Int x, out Int y) {if (b != 0) { Int g = gojo(b, a % b, y, x); y -= (a / b) * x; return g; }x = 1; y = 0; return a;}Int modInv(Int)(Int a, Int m) { Int x, y; gojo(a, m, x, y); return mod(x, m); }long modLogP(long a, long b, long m) {a = mod(a, m); b = mod(b, m);if (m == 1) return 0;long k, ak = 1;Tuple!(long,long)[] as;for (k = 0; k * k < m; ++k) {as ~= tuple(ak, k);ak = (ak * a) % m;}as.sort;ak = modInv(ak, m);for (long i = 0; i < k; ++i) {int pos = as.lowerBound(tuple(b, 0L));if (pos < as.length && as[pos][0] == b) return i * k + as[pos][1];b = (b * ak) % m;}return -1;}long modLog(long a, long b, long m) {a = mod(a, m); b = mod(b, m);long f, g, r = 1 % m;for (f = 0; (g = gcd(a, m)) > 1; ++f) {if (b % g != 0) return (r == b) ? f : -1;b /= g; m /= g;r = (r * (a / g)) % m;}long res = modLogP(a, b * modInv(r, m) % m, m);return (res != -1) ? (f + res) : -1;}enum L = 10L^^5;void main() {try {for (; ; ) {const Mint A = readLong();const Mint B = readLong();const Mint P = readLong();const Mint Q = readLong();long ans = -1;if (B) {/*[ A -B ][ 1 ]*/Mint[2][2] c;c[0][0] = c[1][1] = 1;long[ulong] app;foreach (y; 0 .. L) {const p = c[0][0] * P + c[0][1] * Q;const q = c[1][0] * P + c[1][1] * Q;const key = cast(ulong)(p.x) << 30 | q.x;app[key] = y;debug {if (L - y <= 10) {writeln(y, " ", p, " ", q, " ", key);stdout.flush;}}Mint tmp;tmp = A * c[0][0] - B * c[1][0];c[1][0] = c[0][0];c[0][0] = tmp;tmp = A * c[0][1] - B * c[1][1];c[1][1] = c[0][1];c[0][1] = tmp;}debug {writeln("c = ", c);stdout.flush;}{Mint p = A, q = 2;for (long x = 1; ; ++x) {const pp = c[0][0] * p + c[0][1] * q;const qq = c[1][0] * p + c[1][1] * q;p = pp;q = qq;const key = cast(ulong)(p.x) << 30 | q.x;debug {if (x <= 10) {writeln("! ", p, " ", q, " ", key);stdout.flush;}}if (key in app) {// f^(L x) (A, 2) = f^y (P, Q)const y = app[key];ans = L * x - y + 1;break;}}}} else if (A) {/*X = 0, Y = AP = A^N, Q = A^(N-1)*/assert(P == A * Q);ans = modLogP(A.x, P.x, MO);for (; ans < 2; ans += MO - 1) {}} else {assert(!P);assert(!Q);ans = 2;}writeln(ans);}} catch (EOFException e) {}}