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 uwiuwi
提出日時 2015-07-23 19:18:38
言語 Java19
(openjdk 21)
結果
AC  
実行時間 2,432 ms / 4,000 ms
コード長 12,770 bytes
コンパイル時間 4,241 ms
コンパイル使用メモリ 82,772 KB
実行使用メモリ 63,240 KB
最終ジャッジ日時 2023-09-22 21:43:55
合計ジャッジ時間 12,190 ms
ジャッジサーバーID
(参考情報)
judge14 / judge11
このコードへのチャレンジ(β)

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 2,432 ms
63,120 KB
testcase_01 AC 2,412 ms
63,240 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

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 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	static final int mod = 1000000007;
	
	void solve()
	{
		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);
	}
	
	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];
		}
		gf[0] = 1;
		long[] rigf = rev(inv(gf));
		
		long[] ret = new long[m];
		ret[0] = 1;
		long[] temp = new long[m];
		for(int l = 62;l >= 0;l--){
			if(n<<~l<0){ // +1
				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;
			}
			if(l > 0){ // *2
				long[] ltemp = convolute(ret, ret, 3, mod);
				long[] fu = convolute(Arrays.copyOfRange(ltemp, m, 2*m), rigf, 3, mod);
				long[] last = convolute(co, Arrays.copyOfRange(fu, m, 2*m-1), 3, mod);
				for(int i = 0;i < m;i++){
					ret[i] = last[i] + ltemp[i];
					if(ret[i] >= mod)ret[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 = 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 < f2p.length;j++){
				f2p[j] = -f2p[j];
				if(f2p[j] < 0)f2p[j] += mod;
			}
			for(int j = 0;j < f.length;j++){
				f2p[j] += 2L*f[j];
				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 = {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 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(a.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(a.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(a.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;
	}
	
	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().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)); }
}
0