結果

問題 No.444 旨味の相乗効果
ユーザー uwi
提出日時 2016-11-11 23:02:38
言語 Java
(openjdk 23)
結果
AC  
実行時間 181 ms / 2,500 ms
コード長 7,432 bytes
コンパイル時間 4,610 ms
コンパイル使用メモリ 83,952 KB
実行使用メモリ 42,244 KB
最終ジャッジ日時 2024-06-24 20:53:02
合計ジャッジ時間 7,675 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 5
other AC * 23
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ソースコード

diff #
プレゼンテーションモードにする

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 D {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    void solve()
    {
        int n = ni();
        long C = nl();
        int[] a = na(n);
        long[] dp = new long[n];
        dp[0] = 1;
        int mod = 1000000007;
        long[] rets = new long[200];
        for(int i = 0;i < 200;i++){
            for(int j = n-1;j >= 0;j--){
                for(int k = n-1;k > j;k--){
                    dp[k] += dp[j] * a[k];
                    dp[k] %= mod;
                }
                dp[j] = dp[j] * a[j];
                dp[j] %= mod;
            }
            rets[i] = Arrays.stream(dp).sum() % mod;
        }
        long[] lx = modifiedBerlekampMassey(rets, mod);
        for(int i = 0;i < lx.length;i++){
            lx[i] = (mod-lx[i])%mod;
        }
        lx = Arrays.copyOf(lx, lx.length-1);
        long ret = 0;
        if(lx.length > 0){
            long[] u = lrx(lx, C-1, mod);
            for(int i = u.length-1;i >= 0;i--){
                ret = ret + rets[i] * u[i];
                ret %= mod;
            }
        }
        for(int i = 0;i < n;i++){
            ret -= pow(a[i], C, mod);
        }
        ret %= mod;
        if(ret < 0)ret += mod;
        out.println(ret);
    }
    
    public static long[] lrx(long[] co, long n, long mod)
    {
        long BIG = (Long.MAX_VALUE - 2L*mod*mod)/mod*mod;
        int m = co.length;
        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[][] m2 = new long[m-1][m];
        for(int j = 0;j < m;j++){
            m2[0][j] = co[j];
        }
        for(int i = 1;i < m-1;i++){
            for(int j = 0;j < m;j++){
                long x = m2[i-1][m-1] * co[j];
                if(j-1 >= 0)x += m2[i-1][j-1];
                m2[i][j] = x % mod;
            }
        }
        
        long[] ret = new long[m];
        ret[0] = 1;
        long[] temp = new long[2*m];
        for(int l = 62;l >= 0;l--){
            if(n<<~l<0){
                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){
                Arrays.fill(temp, 0L);
                for(int i = 0;i < m;i++){
                    for(int j = 0;j < m;j++){
                        temp[i+j] += ret[i] * ret[j];
                        if(temp[i+j] >= BIG)temp[i+j] -= BIG;
                    }
                }
                for(int i = 0;i < 2*m-1;i++)temp[i] %= mod;
                for(int i = 0;i < m;i++){
                    long s = temp[i];
                    for(int j = m;j < 2*m-1;j++){
                        s += temp[j] * m2[j-m][i];
                        if(s >= BIG)s -= BIG;
                    }
                    ret[i] = s % mod;
                }
            }
        }
        return ret;
    }
    
    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 long[] modifiedBerlekampMassey(long[] a, int mod)
    {
        assert a.length % 2 == 0;
        int n = a.length/2;
        int m = 2*n-1;
        long[] R0 = new long[2*n+1]; R0[2*n] = 1;
        long[] R1 = new long[2*n];
        for(int i = 0;i < 2*n;i++)R1[i] = a[m-i];
        R1 = strip(R1);
        long[] v0 = {0L};
        long[] v1 = {1L};
        while(n <= R1.length-1){
            long[][] QR = divmod(R0, R1, mod);
            long[] v = sub(v0, mul(QR[0], v1, mod), mod);
            v0 = v1; v1 = v; R0 = R1; R1 = QR[1];
        }
        // normalize
        long z = invl(v1[v1.length-1], mod);
        for(int i = 0;i < v1.length;i++){
            v1[i] = v1[i] * z % mod;
        }
        return strip(v1);
    }
    
    public static long[] mul(long[] a, long[] b, int mod)
    {
        long[] c = new long[a.length+b.length-1];
        for(int i = 0;i < a.length;i++){
            for(int j = 0;j < b.length;j++){
                c[i+j] += a[i] * b[j];
                c[i+j] %= mod;
            }
        }
        return strip(c);
    }
    
    public static long[] sub(long[] a, long[] b, int mod)
    {
        long[] c = Arrays.copyOf(a, Math.max(a.length, b.length));
        for(int i = 0;i < c.length;i++){
            c[i] -= b[i];
            if(c[i] < 0)c[i] += mod;
        }
        return strip(c);
    }
    
    public static long[] strip(long[] a)
    {
        int i;
        for(i = a.length-1;i > 0 && a[i] == 0;i--);
        if(i + 1 == a.length)return a;
        return Arrays.copyOf(a, i+1);
    }
    public static long[][] divmod(long[] A, long[] B, int mod)
    {
        assert B[B.length-1] != 0;
        long[] R = Arrays.copyOf(A, A.length);
        long[] Q = new long[Math.max(1, A.length-B.length+1)];
        long ib = invl(B[B.length-1], mod);
        for(int i = A.length-1, t = Q.length-1;i >= B.length-1;i--,t--){
            long m = R[i] * ib % mod;
            Q[t] = m;
            for(int j = 0, k = i-B.length+1+j;j < B.length;j++,k++){
                R[k] -= B[j] * m;
                R[k] %= mod;
                if(R[k] < 0)R[k] += mod;
            }
            assert R[i] == 0;
        }
        return new long[][]{Q, strip(R)};
    }
    
    
    public 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");
//      Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
//          @Override
//          public void run() {
//              long s = System.currentTimeMillis();
//              solve();
//              out.flush();
//              if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//          }
//      };
//      t.start();
//      t.join();
    }
    
    public static void main(String[] args) throws Exception { new D().run(); }
    
    private byte[] inbuf = new byte[1024];
    public 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 int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private long[] nal(int n)
    {
        long[] a = new long[n];
        for(int i = 0;i < n;i++)a[i] = nl();
        return a;
    }
    
    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[][] nmi(int n, int m) {
        int[][] map = new int[n][];
        for(int i = 0;i < n;i++)map[i] = na(m);
        return map;
    }
    
    private int ni() { return (int)nl(); }
    
    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)); }
}
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