結果

問題 No.125 悪の花弁
ユーザー 37zigen
提出日時 2020-04-22 09:37:43
言語 Java
(openjdk 23)
結果
AC  
実行時間 236 ms / 5,000 ms
コード長 3,499 bytes
コンパイル時間 2,398 ms
コンパイル使用メモリ 79,360 KB
実行使用メモリ 69,916 KB
最終ジャッジ日時 2024-10-11 00:47:33
合計ジャッジ時間 4,451 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
other AC * 6
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 #
プレゼンテーションモードにする

import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Comparator;
import java.util.NoSuchElementException;
public class Main {
    
    public static void main(String[] args) {
        new Main().run();
    }
    
    final long MOD=(long)1e9+7;
    
    int gcd(int a,int b) {
        return a==0?b:gcd(b%a,a);
    }
    
    long pow(long a,long n) {
        return n==0?1:(pow(a*a%MOD,n/2)*(n%2==1?a:1))%MOD;
    }
    
    long inv(long a) {
        return pow(a,MOD-2);
    }
    
    int MAX=(int)1e6+1;
    long[] fac=new long[MAX];
    long[] ifac=new long[MAX];
    int[] cnt_divs=new int[MAX];
    {
        fac[0]=1;
        for (int i=1;i<MAX;++i) fac[i]=i*fac[i-1]%MOD;
        ifac[MAX-1]=inv(fac[MAX-1]);
        for (int i=MAX-1;i>=1;--i) ifac[i-1]=ifac[i]*i%MOD;
        for (int i=2;i<MAX;++i) {
            for (int j=i;j<MAX;j+=i) {
                ++cnt_divs[j];
            }
        }
    }
    
    void run() {
        FastScanner sc=new FastScanner();
        int K=sc.nextInt();
        int[] C=new int[K];
        for (int i=0;i<K;++i) C[i]=sc.nextInt();
        Arrays.sort(C);
        int sumC=(int)Arrays.stream(C).sum();
        int gcd=0;
        for (int i=0;i<K;++i) gcd=gcd(gcd,(int)C[i]);
        long ans=0;
        int[] cnt=new int[gcd+1];
        for (int i=1;i<=gcd;++i) {
            ++cnt[gcd(i,gcd)];
        }
        
        for (int i=1;i<cnt.length;++i) {
            if (cnt[i]==0) continue;
            int num=gcd/i;;
            long add=fac[sumC/num];
            for (int j=0;j<K;++j) {
                add=add*ifac[C[j]/num]%MOD;
            }
            ans=(ans+add*cnt[i]%MOD)%MOD;
        }
        
        ans=ans*inv(sumC)%MOD;
        System.out.println(ans);
    }
    
    void tr(Object...objects) {System.out.println(Arrays.deepToString(objects));}
}
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        return (int)nextLong();
    }
}
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