結果
| 問題 | No.980 Fibonacci Convolution Hard |
| ユーザー |
 CuriousFairy315
|
| 提出日時 | 2020-01-31 22:23:56 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 10,678 bytes |
| コンパイル時間 | 4,355 ms |
| コンパイル使用メモリ | 89,148 KB |
| 実行使用メモリ | 217,204 KB |
| 最終ジャッジ日時 | 2024-09-17 08:50:08 |
| 合計ジャッジ時間 | 11,213 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
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 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
ソースコード
package yukicoder_3679;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class Main3 {
InputStream is;
PrintWriter out;
String INPUT = "";
static final int MOD = 1_000_000_007;
void solve() {
int p = ni(), Q = ni(), max = 2;
int[] q = new int[Q];
for (int i = 0;i < Q;++ i) {
q[i] = ni();
max = Math.max(max, q[i]);
}
long[] fib = new long[max];
fib[1] = 1;
for (int i = 2;i < fib.length;++ i) fib[i] = (p * fib[i - 1] + fib[i - 2]) % MOD;
long[] conv = convolute(fib, fib, 3, MOD);
for (int i : q) {
System.out.println(conv[i - 2]);
}
}
public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};
// public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033};
// public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5};
public static long[] convoluteSimply(long[] a, long[] b, int P, int g) {
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for (int i = 0; i < m; i++ ) {
fa[i] = fa[i] * fb[i] % P;
}
return nttmb(fa, m, true, P, g);
}
public static long[] convolute(long[] a, long[] b) {
int USE = 2;
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
long[][] fs = new long[USE][];
for (int k = 0; k < USE; k++ ) {
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for (int i = 0; i < m; i++ ) {
fa[i] = fa[i] * fb[i] % P;
}
fs[k] = nttmb(fa, m, true, P, g);
}
int[] mods = Arrays.copyOf(NTTPrimes, USE);
long[] gammas = garnerPrepare(mods);
int[] buf = new int[USE];
for (int i = 0; i < fs[0].length; i++ ) {
for (int j = 0; j < USE; j++ )
buf[j] = (int)fs[j][i];
long[] res = garnerBatch(buf, mods, gammas);
long ret = 0;
for (int j = res.length - 1; j >= 0; j-- )
ret = ret * mods[j] + res[j];
fs[0][i] = ret;
}
return fs[0];
}
public static long[] convolute(long[] a, long[] b, int USE, int mod) {
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
long[][] fs = new long[USE][];
for (int k = 0; k < USE; k++ ) {
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for (int i = 0; i < m; i++ ) {
fa[i] = fa[i] * fb[i] % P;
}
fs[k] = nttmb(fa, m, true, P, g);
}
int[] mods = Arrays.copyOf(NTTPrimes, USE);
long[] gammas = garnerPrepare(mods);
int[] buf = new int[USE];
for (int i = 0; i < fs[0].length; i++ ) {
for (int j = 0; j < USE; j++ )
buf[j] = (int)fs[j][i];
long[] res = garnerBatch(buf, mods, gammas);
long ret = 0;
for (int j = res.length - 1; j >= 0; j-- )
ret = (ret * mods[j] + res[j]) % mod;
fs[0][i] = ret;
}
return fs[0];
}
// static int[] wws = new int[270000]; // outer faster
// Modifed Montgomery + Barrett
private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) {
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P) << 1;
int H = Long.numberOfTrailingZeros(K) * 2;
long M = K * K / P;
int[] wws = new int[1 << h - 1];
long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P);
long w = (1L << 32) % P;
for (int k = 0; k < 1 << h - 1; k++ ) {
wws[k] = (int)w;
w = modh(w * dw, M, H, P);
}
long J = invl(P, 1L << 32);
for (int i = 0; i < h; i++ ) {
for (int j = 0; j < 1 << i; j++ ) {
for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++ , s++ , t++ ) {
long u = (dst[s] - dst[t] + 2 * P) * wws[k];
dst[s] += dst[t];
if (dst[s] >= 2 * P) dst[s] -= 2 * P;
// long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
long Q = (u << 32) * J >>> 32;
dst[t] = (u >>> 32) - (Q * P >>> 32) + P;
}
}
if (i < h - 1) {
for (int k = 0; k < 1 << h - i - 2; k++ )
wws[k] = wws[k * 2];
}
}
for (int i = 0; i < n; i++ ) {
if (dst[i] >= P) dst[i] -= P;
}
for (int i = 0; i < n; i++ ) {
int rev = Integer.reverse(i) >>> -h;
if (i < rev) {
long d = dst[i];
dst[i] = dst[rev];
dst[rev] = d;
}
}
if (inverse) {
long in = invl(n, P);
for (int i = 0; i < n; i++ )
dst[i] = modh(dst[i] * in, M, H, P);
}
return dst;
}
// Modified Shoup + Barrett
private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) {
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P) << 1;
int H = Long.numberOfTrailingZeros(K) * 2;
long M = K * K / P;
long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P);
long[] wws = new long[1 << h - 1];
long[] ws = new long[1 << h - 1];
long w = 1;
for (int k = 0; k < 1 << h - 1; k++ ) {
wws[k] = (w << 32) / P;
ws[k] = w;
w = modh(w * dw, M, H, P);
}
for (int i = 0; i < h; i++ ) {
for (int j = 0; j < 1 << i; j++ ) {
for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++ , s++ , t++ ) {
long ndsts = dst[s] + dst[t];
if (ndsts >= 2 * P) ndsts -= 2 * P;
long T = dst[s] - dst[t] + 2 * P;
long Q = wws[k] * T >>> 32;
dst[s] = ndsts;
dst[t] = ws[k] * T - Q * P & (1L << 32) - 1;
}
}
// dw = dw * dw % P;
if (i < h - 1) {
for (int k = 0; k < 1 << h - i - 2; k++ ) {
wws[k] = wws[k * 2];
ws[k] = ws[k * 2];
}
}
}
for (int i = 0; i < n; i++ ) {
if (dst[i] >= P) dst[i] -= P;
}
for (int i = 0; i < n; i++ ) {
int rev = Integer.reverse(i) >>> -h;
if (i < rev) {
long d = dst[i];
dst[i] = dst[rev];
dst[rev] = d;
}
}
if (inverse) {
long in = invl(n, P);
for (int i = 0; i < n; i++ ) {
dst[i] = modh(dst[i] * in, M, H, P);
}
}
return dst;
}
static final long mask = (1L << 31) - 1;
public static long modh(long a, long M, int h, int mod) {
long r = a - ((M * (a & mask) >>> 31) + M * (a >>> 31) >>> h - 31) * mod;
return r < mod ? r : r - mod;
}
private static long[] garnerPrepare(int[] m) {
int n = m.length;
assert n == m.length;
if (n == 0) return new long[0];
long[] gamma = new long[n];
for (int k = 1; k < n; k++ ) {
long prod = 1;
for (int i = 0; i < k; i++ ) {
prod = prod * m[i] % m[k];
}
gamma[k] = invl(prod, m[k]);
}
return gamma;
}
private static long[] garnerBatch(int[] u, int[] m, long[] gamma) {
int n = u.length;
assert n == m.length;
long[] v = new long[n];
v[0] = u[0];
for (int k = 1; k < n; k++ ) {
long temp = v[k - 1];
for (int j = k - 2; j >= 0; j-- ) {
temp = (temp * m[j] + v[j]) % m[k];
}
v[k] = (u[k] - temp) * gamma[k] % m[k];
if (v[k] < 0) v[k] += m[k];
}
return v;
}
public static long invl(long a, long mod) {
long b = mod;
long p = 1, q = 0;
while (b > 0) {
long c = a / b;
long d;
d = a;
a = b;
b = d % b;
d = p;
p = q;
q = d - c * q;
}
return p < 0 ? p + mod : p;
}
public static long pow(long a, long n, long mod) {
// a %= mod;
long ret = 1;
int x = 63 - Long.numberOfLeadingZeros(n);
for (; x >= 0; x-- ) {
ret = ret * ret % mod;
if (n << 63 - x < 0) ret = ret * a % mod;
}
return ret;
}
void run() throws Exception {
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
// @Override
// public void run() {
// long s = System.currentTimeMillis();
// solve();
// out.flush();
// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// }
// };
// t.start();
// t.join();
}
public static void main(String[] args) throws Exception {
new Main3().run();
}
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
private int readByte() {
if (lenbuf == -1) throw new InputMismatchException();
if (ptrbuf >= lenbuf) {
ptrbuf = 0;
try {
lenbuf = is.read(inbuf);
} catch (IOException e) {
throw new InputMismatchException();
}
if (lenbuf <= 0) return -1;
}
return inbuf[ptrbuf++ ];
}
private boolean isSpaceChar(int c) {
return !(c >= 33 && c <= 126);
}
private int skip() {
int b;
while ((b = readByte()) != -1 && isSpaceChar(b));
return b;
}
private double nd() {
return Double.parseDouble(ns());
}
private char nc() {
return (char)skip();
}
private String ns() {
int b = skip();
StringBuilder sb = new StringBuilder();
while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n) {
char[] buf = new char[n];
int b = skip(), p = 0;
while (p < n && !(isSpaceChar(b))) {
buf[p++ ] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private int[] na(int n) {
int[] a = new int[n];
for (int i = 0; i < n; i++ )
a[i] = ni();
return a;
}
private long[] nal(int n) {
long[] a = new long[n];
for (int i = 0; i < n; i++ )
a[i] = nl();
return a;
}
private char[][] nm(int n, int m) {
char[][] map = new char[n][];
for (int i = 0; i < n; i++ )
map[i] = ns(m);
return map;
}
private int[][] nmi(int n, int m) {
int[][] map = new int[n][];
for (int i = 0; i < n; i++ )
map[i] = na(m);
return map;
}
private int ni() {
return (int)nl();
}
private long nl() {
long num = 0;
int b;
boolean minus = false;
while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if (b == '-') {
minus = true;
b = readByte();
}
while (true) {
if (b >= '0' && b <= '9') {
num = num * 10 + (b - '0');
} else {
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) {
System.out.println(Arrays.deepToString(o));
}
}