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 02:34:30 |
言語 | Java21 (openjdk 21) |
結果 |
AC
|
実行時間 | 1,359 ms / 4,000 ms |
コード長 | 16,235 bytes |
コンパイル時間 | 4,673 ms |
コンパイル使用メモリ | 89,368 KB |
実行使用メモリ | 50,124 KB |
最終ジャッジ日時 | 2024-07-17 21:44:52 |
合計ジャッジ時間 | 8,555 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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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 | 1,359 ms
50,080 KB |
testcase_01 | AC | 1,341 ms
50,124 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 = "";// String INPUT = "100000 8 12";// String INPUT = "6 2 0";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];}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 cofor(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][];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*6/7;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){ // +1long 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};// 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};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, cache[k*2], k);long[] fb = 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;}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) * 525860363L % 1051721729L;if(v1 < 0)v1 += 1051721729L;// long temp = (v1 * 1053818881L + v0) % 1045430273L;// long v2 = (fs[2][i] - temp) * 152479290L % 1045430273L;long v2 = ((fs[2][i] + 1045430273L - v0) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L;// if(v2 < 0)v2 += 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;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) * 525860363L % 1051721729L;if(v1 < 0)v1 += 1051721729L;// long temp = (v1 * 1053818881L + v0) % 1045430273L;// long v2 = (fs[2][i] - temp) * 152479290L % 1045430273L;long v2 = ((fs[2][i] + 1045430273L - v0) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L;// if(v2 < 0)v2 += 1045430273L;long ret = (v2 * F + v1 * 1053818881L + v0) % mod;// fs[0][i] = ret;res[i] = ret;}// for(int i = 0;i < fs[0].length;i++){// long v0 = fs[0][i];// long v1 = (fs[1][i] - v0) * 525860363L % 1051721729;// if(v1 < 0)v1 += 1051721729;// long temp = (v1 * 1053818881L + v0) % 1045430273L;// long v2 = (fs[2][i] - temp) * 152479290L % 1045430273L;// if(v2 < 0)v2 += 1045430273L;// long ret = ((v2 * 1051721729L + v1) % mod * 1053818881L + v0) % mod;// fs[0][i] = ret;// }return res;// 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 + Barrettprivate 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&(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 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;}// Modified Shoup + Barrettprivate 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, long[] v){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[] garnerBatch2(int[] u, int[] m, long[] gamma, long[] v){int n = u.length;assert n == m.length;// long[] v = new long[n];v[0] = u[0];{v[1] = (u[1] - v[0]) * gamma[1] % m[1];if(v[1] < 0)v[1] += m[1];}{long temp = (v[1] * m[0] + v[0]) % m[2];v[2] = (u[2] - temp) * gamma[2] % m[2];if(v[2] < 0)v[2] += m[2];}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)); }}