結果
| 問題 |
No.8046 yukicoderの過去問
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2019-04-02 16:10:42 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 8,608 bytes |
| コンパイル時間 | 923 ms |
| コンパイル使用メモリ | 123,700 KB |
| 実行使用メモリ | 13,888 KB |
| 最終ジャッジ日時 | 2024-06-13 04:45:14 |
| 合計ジャッジ時間 | 4,447 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 5 TLE * 1 -- * 3 |
ソースコード
import std.conv, std.functional, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, 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)); }
// a^-1 (mod 2^64)
long modInv(long a)
in {
assert(a & 1, "modInv: a must be odd");
}
do {
long b = ((a << 1) + a) ^ 2;
b *= 2 - a * b;
b *= 2 - a * b;
b *= 2 - a * b;
b *= 2 - a * b;
return b;
}
// 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;
}
}
// 2^-31 a (mod M)
long montgomery(long M)(long a) if (1 <= M && M <= 0x7fffffff && (M & 1))
in {
assert(0 <= a && a < (M << 31), "montgomery: 0 <= a < 2^31 M must hold");
}
do {
enum negInvM = -modInv(M) & 0x7fffffff;
const b = (a + ((a * negInvM) & 0x7fffffff) * M) >> 31;
return (b >= M) ? (b - M) : b;
}
// FFT on Z / M Z with Montgomery multiplication (x -> 2^31 x)
// G: primitive 2^K-th root of unity
class FFT(long M, int K, long G)
if (is(typeof(montgomery!(M)(0))) && K >= 0 && 0 < G && G < M) {
import std.algorithm : swap;
import core.bitop : bsf;
int n, invN;
long[] g;
this(int n)
in {
assert(!(n & (n - 1)), "FFT.this: n must be a power of 2");
assert(4 <= n && n <= 1 << K, "FFT.this: 4 <= n <= 2^K must hold");
}
do {
this.n = n;
this.invN = ((1L << 31) / n) % M;
g.length = n + 1;
g[0] = (1L << 31) % M;
g[1] = (G << 31) % M;
foreach (_; 0 .. K - bsf(n)) {
g[1] = montgomery!(M)(g[1] * g[1]);
}
foreach (i; 2 .. n + 1) {
g[i] = montgomery!(M)(g[i - 1] * g[1]);
}
assert(g[0] != g[n >> 1] && g[0] == g[n],
"FFT.this: G must be a primitive 2^K-th root of unity");
for (int i = 0, j = 0; i < n >> 1; ++i) {
if (i < j) {
swap(g[i], g[j]);
swap(g[n - i], g[n - j]);
}
for (int m = n >> 1; (m >>= 1) && !((j ^= m) & m); ) {}
}
}
void fftMontgomery(long[] x, bool inv)
in {
assert(x.length == n, "FFT.fftMontgomery: |x| = n must hold");
}
do {
foreach_reverse (h; 0 .. bsf(n)) {
const l = 1 << h;
foreach (i; 0 .. n >> 1 >> h) {
const gI = g[inv ? (n - i) : i];
foreach (j; i << 1 << h .. ((i << 1) + 1) << h) {
const t = montgomery!(M)(gI * x[j + l]);
if ((x[j + l] = x[j] - t) < 0) {
x[j + l] += M;
}
if ((x[j] += t) >= M) {
x[j] -= M;
}
}
}
}
for (int i = 0, j = 0; i < n; ++i) {
if (i < j) {
swap(x[i], x[j]);
}
for (int m = n; (m >>= 1) && !((j ^= m) & m); ) {}
}
if (inv) {
foreach (i; 0 .. n) {
x[i] = montgomery!(M)(invN * x[i]);
}
}
}
long[] convolution(long[] a, long[] b)
in {
assert(a.length <= n, "FFT.convolution: |a| <= n must hold");
assert(b.length <= n, "FFT.convolution: |b| <= n must hold");
}
do {
auto x = new long[n], y = new long[n];
foreach (i; 0 .. a.length) {
const t = a[i] % M;
x[i] = (((t < 0) ? (t + M) : t) << 31) % M;
}
foreach (i; 0 .. b.length) {
const t = b[i] % M;
y[i] = (((t < 0) ? (t + M) : t) << 31) % M;
}
fftMontgomery(x, false);
fftMontgomery(y, false);
foreach (i; 0 .. n) {
x[i] = montgomery!(M)(x[i] * y[i]);
}
fftMontgomery(x, true);
foreach (i; 0 .. n) {
x[i] = montgomery!(M)(x[i]);
}
return x;
}
}
// P0 P1 P2 > 2^90, P0 + P1 + P2 = 2^32 + 3
enum FFT_P0 = 2013265921L; // 2^27 15 + 1
enum FFT_P1 = 1811939329L; // 2^26 27 + 1
enum FFT_P2 = 469762049L; // 2^26 7 + 1
alias FFT0 = FFT!(FFT_P0, 27, 440564289L); // 31^15
alias FFT1 = FFT!(FFT_P1, 26, 72705542L); // 13^27
alias FFT2 = FFT!(FFT_P2, 26, 2187L); // 3^ 7
// Convolution of a and b (indices mod fft0.n)
// modify a and b so that 0 <= a[i] < m, 0 <= b[i] < m
long[] convolution(FFT0 fft0, FFT1 fft1, FFT2 fft2, long[] a, long[] b, long m)
in {
assert(fft0.n == fft1.n && fft0.n == fft2.n, "convolution: fft0.n = fft1.n = fft2.n must hold");
assert(1 <= m && m <= 0x7fffffff, "convolution: 1 <= m < 2^31 must hold");
}
do {
enum FFT_INV01 = modInv(FFT_P0, FFT_P1);
enum FFT_INV012 = modInv(FFT_P0 * FFT_P1, FFT_P2);
foreach (i; 0 .. a.length) {
if ((a[i] %= m) < 0) {
a[i] += m;
}
}
foreach (i; 0 .. b.length) {
if ((b[i] %= m) < 0) {
b[i] += m;
}
}
const x0 = fft0.convolution(a, b);
const x1 = fft1.convolution(a, b);
const x2 = fft2.convolution(a, b);
auto x = new long[fft0.n];
foreach (i; 0 .. fft0.n) {
auto y0 = x0[i] % FFT_P0;
auto y1 = (FFT_INV01 * (x1[i] - y0)) % FFT_P1;
if (y1 < 0) {
y1 += FFT_P1;
}
auto y2 = (FFT_INV012 * ((x2[i] - y0 - FFT_P0 * y1) % FFT_P2)) % FFT_P2;
if (y2 < 0) {
y2 += FFT_P2;
}
x[i] = (y0 + FFT_P0 * y1 + ((FFT_P0 * FFT_P1) % m) * y2) % m;
}
return x;
}
// X^k mod f(X), coefficients in Z / m Z
// f: monic (array length: deg f)
long[] polyPower(long k, long[] f, long m)
in {
assert(k >= 0, "polyPower: k >= 0 must hold");
assert(f.length >= 1, "polyPower: deg f >= 1 must hold");
assert(1 <= m && m <= 0x7fffffff, "polyPower: 1 <= m < 2^31 must hold");
}
do {
import std.algorithm.comparison : min;
import core.bitop : bsr;
const n = cast(int)(f.length);
auto fRev = new long[n + 1];
fRev[0] = 1;
foreach (i; 1 .. n + 1) {
fRev[i] = f[n - i];
}
auto negInvFRev = [m - 1];
for (int l = 1; l < n; l <<= 1) {
auto fft0 = new FFT0(l << 2), fft1 = new FFT1(l << 2), fft2 = new FFT2(l << 2);
auto t = convolution(fft0, fft1, fft2, fRev[0 .. min(l << 1, n + 1)], negInvFRev, m)[0 .. l << 1];
t[0] += 2;
negInvFRev = convolution(fft0, fft1, fft2, negInvFRev, t, m)[0 .. l << 1];
}
auto a = new long[n];
if ((a[0] = 1) >= m) {
a[0] -= m;
}
if (k > 0) {
int nn;
for (nn = 4; nn < 2 * n; nn <<= 1) {}
auto fft0 = new FFT0(nn), fft1 = new FFT1(nn), fft2 = new FFT2(nn);
foreach_reverse (h; 0 .. bsr(k) + 1) {
a = convolution(fft0, fft1, fft2, a, a, m);
auto aRev = new long[n];
foreach (i; 0 .. n) {
aRev[i] = a[2 * n - 1 - i];
}
auto negRevQ = convolution(fft0, fft1, fft2, aRev, negInvFRev, m);
auto negQ = new long[n];
foreach (i; 0 .. n) {
negQ[i] = negRevQ[n - 1 - i];
}
auto t = convolution(fft0, fft1, fft2, f, negQ, m);
foreach (i; 0 .. n) {
if ((a[i] += t[i]) >= m) {
a[i] -= m;
}
}
a.length = n;
if ((k >> h) & 1) {
a = [0L] ~ a;
foreach (i; 0 .. n) {
if (((a[i] -= a[n] * f[i]) %= m) < 0) {
a[i] += m;
}
}
a.length = n;
}
}
}
return a;
}
enum MO = 10L^^9 + 7;
int K;
int N;
int[] X;
void main() {
try {
for (; ; ) {
K = readInt();
N = readInt();
X = new int[N];
foreach (i; 0 .. N) {
X[i] = readInt();
}
const d = X[$ - 1];
auto f = new long[d];
foreach (i; 0 .. N) {
f[d - X[i]] -= 1;
}
auto g = polyPower(K + d - 1, f, MO);
writeln(g[d - 1]);
}
} catch (EOFException e) {
}
}