結果
問題 | No.950 行列累乗 |
ユーザー |
👑 |
提出日時 | 2019-12-13 02:16:53 |
言語 | D (dmd 2.109.1) |
結果 |
WA
|
実行時間 | - |
コード長 | 8,123 bytes |
コンパイル時間 | 1,369 ms |
コンパイル使用メモリ | 139,236 KB |
実行使用メモリ | 20,504 KB |
最終ジャッジ日時 | 2024-06-22 03:33:25 |
合計ジャッジ時間 | 6,904 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 56 WA * 1 |
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, core.stdc.stdlib;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)); }// floor(a^(1/k))ulong floorKthRoot(ulong a, ulong k) {import core.bitop : bsr;import std.algorithm : min;if (a == 0) {return 0;} else if (k <= 1) {return a;} else if (k == 2) {ulong 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;} else if (k <= 40) {// min x s.t. x^k >= 2^64enum ulong[] HIS =[0, 0, 4294967296UL, 2642246, 65536, 7132, 1626, 566, 256, 139, 85, 57,41, 31, 24, 20, 16, 14, 12, 11, 10, 9, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5,4, 4, 4, 4, 4, 4, 4, 4, 4];ulong lo = 1UL << (bsr(a) / k);ulong hi = min(1UL << (bsr(a) / k + 1), HIS[cast(size_t)(k)]);for (; lo + 1 < hi; ) {const ulong mid = (lo + hi) / 2;ulong b = mid * mid;foreach (i; 2 .. k) b *= mid;((b <= a) ? lo : hi) = mid;}return lo;} else if (k <= 63) {return ((1UL << k) <= a) ? 2 : 1;} else {return 1;}}// a^-1 (mod m)long modInv(long a, long m)in {assert(m > 0, "modInv: m > 0 must hold");}do {long b = m, x = 1, y = 0, t;for (; ; ) {t = a / b; a -= t * b;if (a == 0) {assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");if (b == -1) y = -y;return (y < 0) ? (y + m) : y;}x -= t * y;t = b / a; b -= t * a;if (b == 0) {assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");if (a == -1) x = -x;return (x < 0) ? (x + m) : x;}y -= t * x;}}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, al = 1;Tuple!(long,long)[] as;for (k = 0; k * k < m; ++k) {as ~= tuple(al, k);al = (al * a) % m;}as.sort;al = modInv(al, 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 * al) % m;}return -1;}long P;long[][] A, B;long[][] div(long[][] a, long t) {const invT = modInv(t, P);auto b = new long[][](2, 2);foreach (i; 0 .. 2) foreach (j; 0 .. 2) {b[i][j] = mod(invT * a[i][j], P);}return b;}long[][] inv(long[][] a) {const det = mod(a[0][0] * a[1][1] - a[0][1] * a[1][0], P);return div([[a[1][1], -a[0][1]], [-a[1][0], a[0][0]]], det);}long[][] mul(long[][] a, long[][] b) {auto c = new long[][](2, 2);foreach (i; 0 .. 2) foreach (k; 0 .. 2) foreach (j; 0 .. 2) {c[i][j] = mod(c[i][j] + a[i][k] * b[k][j], P);}return c;}long[][] power(long[][] a, long e) {long[][] b = a, c = [[1, 0], [0, 1]];for (; e; e >>= 1) {if (e & 1) c = mul(c, b);b = mul(b, b);}return c;}long solveBSGS(long[][] a, long[][] b) {const m = cast(int)(floorKthRoot(2 * P, 2) + 2);auto als = new Tuple!(long[][], int)[m];long[][] al = [[1, 0], [0, 1]];foreach (l; 0 .. m) {als[l] = tuple(al, l);al = mul(al, a);}als.sort;al = inv(al);long[][] amk = b;foreach (k; 0 .. m) {const pos = als.lowerBound(tuple(amk, 0));if (pos < m && als[pos][0] == amk) {return k * cast(long)(m) + als[pos][1];}amk = mul(amk, al);}return -1;}void main() {try {for (; ; ) {P = readLong();A = new long[][](2, 2);foreach (i; 0 .. 2) foreach (j; 0 .. 2) {A[i][j] = readLong();}B = new long[][](2, 2);foreach (i; 0 .. 2) foreach (j; 0 .. 2) {B[i][j] = readLong();}long ans;const detA = mod(A[0][0] * A[1][1] - A[0][1] * A[1][0], P);const detB = mod(B[0][0] * B[1][1] - B[0][1] * B[1][0], P);if (detA == 0) {if (detB == 0) {if (A == [[0, 0], [0, 0]]) {if (B == [[0, 0], [0, 0]]) {ans = 1;} else {ans = -1;}} else {/*C^-1 A C = [[r, 0], [0, 0]]a00 c00 + a01 c10 = r c00a10 c00 + a11 c10 = r c10a00 c01 + a01 c11 = 0a10 c01 + a11 c11 = 0*/const r = mod(A[0][0] + A[1][1], P);assert(r != 0);auto c = new long[][](2, 2);c[0][0] = mod(-A[0][1], P);c[1][0] = mod(A[0][0] - r, P);if (c[0][0] == 0 && c[1][0] == 0) {c[0][0] = mod(-(A[1][1] - r), P);c[1][0] = mod(A[1][0], P);}if (c[0][0] == 0 && c[1][0] == 0) {assert(false);}c[0][1] = mod(-A[0][1], P);c[1][1] = mod(A[0][0], P);if (c[0][1] == 0 && c[1][1] == 0) {c[0][1] = mod(-A[1][1], P);c[1][1] = mod(A[1][0], P);}if (c[0][1] == 0 && c[1][1] == 0) {assert(false);}debug {writeln("r = ", r);writeln("c = ", c);}auto a = mul(mul(inv(c), A), c);auto b = mul(mul(inv(c), B), c);debug {writeln("a = ", a);writeln("b = ", b);}assert(a == [[r, 0L], [0L, 0L]]);if (b[0][1] == 0 && b[1][0] == 0 && b[1][1] == 0) {const res = modLogP(a[0][0], mod(b[0][0] * modInv(a[0][0], P), P), P);if (res == -1) {ans = -1;} else {ans = res + 1;}} else {ans = -1;}}} else {ans = -1;}} else {const period = modLogP(detA, modInv(detA, P), P) + 1;long e0 = modLogP(detA, detB, P);debug {writeln("detA = ", detA, ", detB = ", detB);writeln("period = ", period);writeln("e0 = ", e0);}if (e0 == -1) {ans = -1;} else {if (e0 == 0) {e0 += period;}auto a = power(A, period);auto b = mul(B, inv(power(A, e0)));debug {writeln("a = ", a);writeln("b = ", b);}const res = solveBSGS(a, b);if (res == -1) {ans = -1;} else {ans = e0 + period * res;}}}writeln(ans);}} catch (EOFException e) {}}