結果
| 問題 | No.214 素数サイコロと合成数サイコロ (3-Medium) |
| ユーザー |
 uwi
|
| 提出日時 | 2015-07-28 22:56:12 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 691 ms / 3,000 ms |
| コード長 | 14,994 bytes |
| コンパイル時間 | 4,431 ms |
| コンパイル使用メモリ | 89,808 KB |
| 実行使用メモリ | 58,136 KB |
| 最終ジャッジ日時 | 2024-07-17 13:26:25 |
| 合計ジャッジ時間 | 7,707 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（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 | 654 ms
58,136 KB |
| testcase_01 | AC | 615 ms
57,888 KB |
| testcase_02 | AC | 691 ms
57,920 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_5 {
InputStream is;
PrintWriter out;
String INPUT = "";
static final int mod = 1000000007;
void solve()
{
superPrepare();
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);
long[] co = rstrip(convolute(pp, cc, 3, mod));
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);
long[] xco = lr(co, co.length-1+n);
long ret = 0;
for(long v : xco)ret += v;
out.println(ret%mod);
}
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 = max;i >= 0;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];
if(ret[i] >= mod)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++){
gf[i+1] = (mod-co[m-1-i]) % mod;
}
gf[0] = 1;
long[] rigf = rev(inv(gf));
int mm = Math.max(2, Integer.highestOneBit(m-1)<<2);
long[][] frigf = new long[3][mm];
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[] ret = new long[m];
ret[0] = 1;
int h = 63-Long.numberOfLeadingZeros(n);
int hh = h*6/7;
for(int u = 0;u < n>>>hh;u++){
long r = ret[m-1];
for(int i = m-1;i >= 1;i--){
ret[i] = (r * co[i] + ret[i-1]) % mod;
}
ret[0] = r * co[0] % mod;
// for(int i = 0;i < m;i++)temp[i] = ret[m-1] * co[i];
// for(int i = 1;i < m;i++)temp[i] += ret[i-1];
// for(int i = 0;i < m;i++)ret[i] = temp[i] % 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 >= 1;i--){
ret[i] = (r * co[i] + ret[i-1]) % mod;
}
ret[0] = r * co[0] % mod;
// for(int i = 0;i < m;i++)temp[i] = ret[m-1] * co[i];
// for(int i = 1;i < m;i++)temp[i] += ret[i-1];
// for(int i = 0;i < m;i++)ret[i] = temp[i] % 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};
// 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[] 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);
}
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 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;
fa[i] = modh(fa[i]*fb[i], M, H, P);
}
fs[k] = nttmb(fa, m, true, P, g, k);
}
long K = Integer.highestOneBit(mod)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/mod;
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;
for(int j = res.length-1;j >= 0;j--)ret = modh(ret * mods[j] + res[j], M, H, mod);
fs[0][i] = ret;
}
return fs[0];
}
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);
Arrays.fill(dst, 0);
System.arraycopy(src, 0, dst, 0, Math.min(n, src.length));
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
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&(1L<<32)-1)*J&(1L<<32)-1;
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 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;
}
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_5().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 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 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[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
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)); }
}