結果
問題 | No.950 行列累乗 |
ユーザー |
👑 |
提出日時 | 2019-12-13 01:15:36 |
言語 | D (dmd 2.109.1) |
結果 |
RE
|
実行時間 | - |
コード長 | 9,673 bytes |
コンパイル時間 | 1,277 ms |
コンパイル使用メモリ | 143,148 KB |
実行使用メモリ | 13,540 KB |
最終ジャッジ日時 | 2024-06-22 03:31:00 |
合計ジャッジ時間 | 7,023 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 * 2 RE * 2 |
other | AC * 19 WA * 9 RE * 29 |
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)); }// 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;}}// xorshiftuint xrand() {static uint x = 314159265, y = 358979323, z = 846264338, w = 327950288;uint t = x ^ x << 11; x = y; y = z; z = w; return w = w ^ w >> 19 ^ t ^ t >> 8;}// 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;}}// (a / 2) mod mlong div2(long a, long m)in {assert(1 <= m && m < 1L << 62, "div2: 1 <= m < 2^62 must hold");assert(m % 2 != 0, "div2: m must not be divisibly by 3");assert(0 <= a && a < m, "div2: 0 <= a < m must hold");}do {return (a + (a % 2) * m) / 2;}// (a / 3) mod mlong div3(long a, long m)in {assert(1 <= m && m < 1L << 61, "div3: 1 <= m < 2^61 must hold");assert(m % 3 != 0, "div3: m must not be divisibly by 3");assert(0 <= a && a < m, "div3: 0 <= a < m must hold");}do {return (a + (((3 - a % 3) * (m % 3)) % 3) * m) / 3;}// Jacobi symbol (a/m)int jacobi(long a, long m)in {assert(m > 0, "jacobi: m > 0 must hold");assert(m & 1, "jacobi: m must be odd");}do {import core.bitop : bsf;import std.algorithm.mutation : swap;int s = 1;if (a < 0) a = a % m + m;for (; m > 1; ) {a %= m;if (a == 0) return 0;const r = bsf(a);if ((r & 1) && ((m + 2) & 4)) s = -s;a >>= r;if (a & m & 2) s = -s;swap(a, m);}return s;}// sqrt(a) (mod p)// p: be prime// (b + sqrt(b^2 - a))^((p+1)/2) in F_p(sqrt(b^2 - a))long[] modSqrt(long a, long p)in {assert(p < 1L << 31, "modSqrt: p < 2^31 must hold");assert(-p * p <= a && a <= p * p, "modSqrt: -p^2 <= a <= p^2 must hold");}do {if (p == 2) return [a & 1];const j = jacobi(a, p);if (j == 0) return [0];if (j == -1) return [];long b, d;for (; ; ) {b = xrand() % p;d = (b * b - a) % p;if (d < 0) d += p;if (jacobi(d, p) == -1) break;}long[2] mul(in long[2] x, in long[2] y) {return [(x[0] * y[0] + d * ((x[1] * y[1]) % p)) % p,(x[0] * y[1] + x[1] * y[0]) % p];}long[2] f = [b, 1], g = [1, 0];for (long e = (p + 1) >> 1; e; e >>= 1) {if (e & 1) g = mul(g, f);f = mul(f, f);}assert(g[1] == 0);return (g[0] < p - g[0]) ? [g[0], p - g[0]] : [p - g[0], g[0]];}// Roots of f0 + f1 T + T^2 in F_p[T] with multiplicity// p: primelong[] modRoots2(long f0, long f1, long p)in {assert(2 <= p && p < 1L << 31, "modRoots2: 2 <= p < 2^31 must hold");assert(0 <= f0 && f0 < p, "modRoots2: 0 <= f0 < p must hold");assert(0 <= f1 && f1 < p, "modRoots2: 0 <= f1 < p must hold");}do {import std.algorithm : sort;if (p == 2) {if (f0 == 0 && f1 == 0) return [0, 0];if (f0 == 0 && f1 == 1) return [0, 1];if (f0 == 1 && f1 == 0) return [1, 1];return [];} else {const f12 = f1.div2(p);auto ts = modSqrt(f12 * f12 - f0, p);foreach (ref t; ts) {if ((t -= f12) < 0) t += p;}sort(ts);switch (ts.length) {case 0: return [];case 1: return [ts[0], ts[0]];case 2: return ts;default: assert(false);}}}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 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;}long P;long[][] A, B;long detA;long[][] inv(long[][] a) {const det = mod(a[0][0] * a[1][1] - a[0][1] * a[1][0], P);const t = modInv(det, P);auto b = [[a[1][1], -a[0][1]], [-a[1][0], a[0][0]]];foreach (i; 0 .. 2) foreach (j; 0 .. 2) {b[i][j] = mod(t * b[i][j], P);}return b;}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 solveBBGS() {assert(detA != 0);const m = cast(int)(floorKthRoot(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;auto invA = inv(A);auto invAm = inv(al);long[][] amk = B;amk = mul(amk, invA);foreach (k; 0 .. m) {const pos = als.lowerBound(tuple(amk, 0));if (pos < m && als[pos][0] == amk) {return 1 + k * cast(long)(m) + als[pos][1];}amk = mul(amk, invAm);}return -1;}/*c^-1 A c = [[r, u], [0, s]]a00 c00 + a01 c10 = c00 ra10 c00 + a11 c10 = c10 ra00 c01 + a01 c11 = c01 s + c00 ua10 c01 + a11 c11 = c11 s + c10 u*/long[][] getTr(long[] ts) {auto c = new long[][](2, 2);// tasuketereturn null;}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();}detA = mod(A[0][0] * A[1][1] - A[0][1] * A[1][0], P);// (A[0][0] - T) (A[1][1] - T) - A[0][1] * A[1][0]auto ts = modRoots2(detA, mod(-(A[0][0] + A[1][1]), P), P);debug {writeln("ts = ", ts);}long ans;if (ts.length == 2) {if (ts[0] == ts[1]) {// yabaiauto c = getTr(ts);auto invC = inv(c);auto a = mul(mul(invC, A), c);auto b = mul(mul(invC, B), c);debug {writeln("a = ", a);writeln("b = ", b);}import core.stdc.stdlib;exit(1);} else {if (ts[0] == 0 && ts[1] == 0) {// zeroif (B[0][0] == 0 && B[0][1] == 0 && B[1][0] == 0 && B[1][1] == 0) {ans = 1;} else {ans = -1;}} else if (ts[0] == 0) {// ?import core.stdc.stdlib;exit(1);} else {ans = solveBBGS();}}} else {ans = solveBBGS();}writeln(ans);}} catch (EOFException e) {}}