結果
| 問題 | No.215 素数サイコロと合成数サイコロ (3-Hard) |
| ユーザー |
 uwi
|
| 提出日時 | 2015-07-29 16:19:47 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 1,447 ms / 4,000 ms |
| コード長 | 12,161 bytes |
| コンパイル時間 | 5,501 ms |
| コンパイル使用メモリ | 89,812 KB |
| 実行使用メモリ | 59,628 KB |
| 最終ジャッジ日時 | 2024-07-17 22:06:42 |
| 合計ジャッジ時間 | 9,283 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（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 | AC | 1,447 ms
59,628 KB |
| testcase_01 | AC | 1,388 ms
59,140 KB |
ソースコード
package q4xx;
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 Q444_5S {
InputStream is;
PrintWriter out;
String INPUT = "";
// String INPUT = "100000 8 12";
// String INPUT = "6 2 0";
static final int mod = 1000000007;
void solve()
{
// long S = System.nanoTime();
superPrepare();
// tr(System.nanoTime() - S);
long n = nl();
int P = ni(), C = ni();
long[] pp = make(new int[]{2, 3, 5, 7, 11, 13}, P);
long[] cc = make(new int[]{4, 6, 8, 9, 10, 12}, C);
// tr(System.nanoTime() - S);
long[] co = rstrip(convolute(pp, cc, 3, mod));
// tr(System.nanoTime() - S);
for(int i = 0, j = co.length-1;i < j;i++,j--){
long d = co[i]; co[i] = co[j]; co[j] = d;
}
co = Arrays.copyOf(co, co.length-1);
// tr(System.nanoTime() - S);
long[] xco = lr(co, co.length-1+n);
// tr(System.nanoTime() - S);
long ret = 0;
for(long v : xco)ret += v;
out.println(ret%mod);
// tr(System.nanoTime() - S);
}
static long[] rstrip(long[] a)
{
for(int i = a.length-1;i >= 0;i--){
if(a[i] != 0)return Arrays.copyOf(a, i+1);
}
return new long[0];
}
long[] make(int[] ps, int P)
{
int max = P*ps[ps.length-1];
int[][] dp = new int[max+1][6];
dp[0][0] = 1;
for(int k = 0;k < P;k++){
for(int i = ps[ps.length-1]*k;i >= ps[0]*k;i--){
long s = 0;
for(int j = 0;j < 6;j++){
s += dp[i][j];
if(s >= mod)s -= mod;
dp[i][j] = 0;
if(i+ps[j] <= max){
dp[i+ps[j]][j] += s;
if(dp[i+ps[j]][j] >= mod)dp[i+ps[j]][j] -= mod;
}
}
}
}
long[] ret = new long[max+1];
for(int i = 0;i <= max;i++){
for(int j = 0;j < 6;j++){
ret[i] += dp[i][j];
}
ret[i] %= mod;
}
return ret;
}
public static long f(long[] a, long[] co)
{
long big = 8L*mod*mod;
long s = 0;
for(int i = 0;i < co.length;i++){
s += co[i] * a[i];
if(s >= big)s -= big;
}
return s % mod;
}
static long[] rev(long[] a)
{
for(int i = 0, j = a.length-1;i < j;i++,j--){
long d = a[i]; a[i] = a[j]; a[j] = d;
}
return a;
}
public static long[] lr(long[] co, long n)
{
int m = co.length;
if(m == 0)return new long[0];
if(m == 1){
long ret = 1;
long mul = co[0];
for(;n > 0;n >>>= 1){
if((n&1)==1)ret = ret * mul % mod;
mul = mul * mul % mod;
}
return new long[]{ret};
}
long[] gf = new long[m+1]; // Generating Function of co
for(int i = 0;i < m;i++){
if(co[m-1-i] == 0)continue;
gf[i+1] = mod-co[m-1-i];
}
gf[0] = 1;
long[] rigf = rev(inv(gf));
int mm = Math.max(2, Integer.highestOneBit(m-1)<<2);
long[][] frigf = new long[3][];
for(int k = 0;k < 3;k++){
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
frigf[k] = nttmb(rigf, mm, false, P, g, k);
}
long[][] fco = new long[3][];
for(int k = 0;k < 3;k++){
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
fco[k] = nttmb(co, mm, false, P, g, k);
}
long K = Integer.highestOneBit(mod)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/mod;
long[] ret = new long[m];
ret[0] = 1;
int h = 63-Long.numberOfLeadingZeros(n);
int hh = h*8/9;
int las = m-1;
while(co[las] == 0)las--;
for(int u = 0;u < n>>>hh;u++){
long r = ret[m-1];
for(int i = m-1;i > las;i--){
ret[i] = ret[i-1];
}
for(int i = las;i >= 1;i--){
ret[i] = modh(r * co[i] + ret[i-1], M, H, mod);
}
ret[0] = modh(r * co[0], M, H, mod);
}
for(int l = hh-1;l >= 0;l--){
long[] ltemp = convolute(ret, ret, 3, mod, null);
long[] fu = convolute(Arrays.copyOfRange(ltemp, m, 2*m), rigf, 3, mod, frigf);
long[] last = convolute(Arrays.copyOfRange(fu, m, 2*m), co, 3, mod, fco);
for(int i = 0;i < m;i++){
ret[i] = last[i] + ltemp[i];
if(ret[i] >= mod)ret[i] -= mod;
}
if(n<<~l<0){ // +1
long r = ret[m-1];
for(int i = m-1;i > las;i--){
ret[i] = ret[i-1];
}
for(int i = las;i >= 1;i--){
ret[i] = modh(r * co[i] + ret[i-1], M, H, mod);
}
ret[0] = modh(r * co[0], M, H, mod);
}
}
return ret;
}
// public static long[] mul(long[] a, long[] b, int lim)
// {
// return Arrays.copyOf(NTTCRT.convoluteSimply(a, b, mod, G), lim);
// }
public static long[] mul(long[] a, long[] b, int lim)
{
return Arrays.copyOf(convolute(a, b, 3, mod), lim);
}
// F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x)
public static long[] inv(long[] p)
{
int n = p.length;
long[] f = {invl(p[0], mod)};
for(int i = 0;i < p.length;i++){
if(p[i] == 0)continue;
p[i] = mod-p[i];
}
for(int i = 1;i < 2*n;i*=2){
long[] f2 = mul(f, f, Math.min(n, 2*i));
long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i));
for(int j = 0;j < f.length;j++){
f2p[j] += 2L*f[j];
if(f2p[j] >= mod)f2p[j] -= mod;
if(f2p[j] >= mod)f2p[j] -= mod;
}
f = f2p;
}
return f;
}
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 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};
static long F = 1051721729L * 1053818881L % mod;
public static long[] convolute(long[] a, long[] b, int USE, int mod)
{
int m = Math.max(2, Integer.highestOneBit(a.length+b.length-1)<<1);
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, k);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g, k);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
fs[k] = nttmb(fa, m, true, P, g, k);
}
long[] res = new long[a.length+b.length-1];
for(int i = 0;i < res.length;i++){
long v0 = fs[0][i];
long v1 = (fs[1][i] - v0 + 1051721729L + 1051721729L) * 525860363L % 1051721729L;
// if(v1 < 0)v1 += 1051721729L;
long v2 = ((fs[2][i] - v0 + 1045430273L) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L;
long ret = (v2 * F + v1 * 1053818881L + v0) % mod;
res[i] = ret;
}
return res;
}
static long[][] cache = new long[6][16384];
public static long[] convolute(long[] a, long[] b, int USE, int mod, long[][] ffb)
{
int m = ffb != null ? ffb[0].length : Math.max(2, Integer.highestOneBit(a.length+b.length-1)<<1);
long[][] fs = new long[USE][];
for(int k = 0;k < USE;k++){
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
long[] fa = nttmb(a, m, false, P, g, cache[k*2], k);
long[] fb = ffb != null ? ffb[k] : a == b ? fa : nttmb(b, m, false, P, g, cache[k*2+1], k);
for(int i = 0;i < m;i++){
// fa[i] = fa[i]*fb[i]%P;
long z = fa[i]*fb[i];
long r = z-((M*(z&mask)>>>31)+M*(z>>>31)>>>H-31)*P;
fa[i] = r;
// fa[i] = modh(fa[i]*fb[i], M, H, P);
}
fs[k] = nttmb(fa, m, true, P, g, k);
}
// mods={1053818881, 1051721729, 1045430273
// gamma=[[0, 525860363, 152479290]]
// tr(1053818881L * 152479290L % 1045430273L);
long[] res = new long[a.length+b.length-1];
for(int i = 0;i < res.length;i++){
long v0 = fs[0][i];
long v1 = (fs[1][i] - v0 + 1051721729L + 1051721729L) * 525860363L % 1051721729L;
// if(v1 < 0)v1 += 1051721729L;
long v2 = ((fs[2][i] - v0 + 1045430273L) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L;
long ret = (v2 * F + v1 * 1053818881L + v0) % mod;
res[i] = ret;
}
return res;
}
static int L = 14;
static int[][][] wws;
static int[][][] iwws;
static void superPrepare()
{
wws = new int[3][][];
iwws = new int[3][][];
for(int t = 0;t < 3;t++){
int P = NTTPrimes[t], g = NTTPrimitiveRoots[t];
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
{
wws[t] = new int[L+1][];
long w = (1L<<32)%P;
long dw = pow(g, P-1>>>L, P);
wws[t][L] = new int[1<<L-1];
for(int k = 0;k < 1<<L-1;k++){
wws[t][L][k] = (int)w;
w = modh(w*dw, M, H, P);
}
for(int i = L-1;i >= 1;i--){
wws[t][i] = new int[1<<i-1];
for(int k = 0;k < 1<<i-1;k++)wws[t][i][k] = wws[t][i+1][k*2];
}
}
{
iwws[t] = new int[L+1][];
long w = (1L<<32)%P;
long dw = pow(g, P-1-(P-1>>>L), P);
iwws[t][L] = new int[1<<L-1];
for(int k = 0;k < 1<<L-1;k++){
iwws[t][L][k] = (int)w;
w = modh(w*dw, M, H, P);
}
for(int i = L-1;i >= 1;i--){
iwws[t][i] = new int[1<<i-1];
for(int k = 0;k < 1<<i-1;k++)iwws[t][i][k] = iwws[t][i+1][k*2];
}
}
}
}
private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g, int ind){
return nttmb(src, n, inverse, P, g, new long[n], ind);
}
// Modifed Montgomery + Barrett
private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g, long[] dst, int ind)
{
// long[] dst = Arrays.copyOf(src, n);
System.arraycopy(src, 0, dst, 0, Math.min(n, src.length));
Arrays.fill(dst, Math.min(n, src.length), n, 0);
int h = Integer.numberOfTrailingZeros(n);
long J = invl(P, 1L<<32);
int[][] mul = inverse ? iwws[ind] : wws[ind];
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)*mul[h-i][k];
dst[s] += dst[t];
if(dst[s] >= 2*P)dst[s] -= 2*P;
long Q = (u<<32)*J>>>32;
dst[t] = (u>>>32)-(Q*P>>>32)+P;
}
}
}
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 K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
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 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");
}
public static void main(String[] args) throws Exception { new Q444_5S().run(); }
private byte[] inbuf = new byte[1024];
private 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 int ni()
{
int num = 0, 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 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)); }
}