結果

問題 No.665 Bernoulli Bernoulli
コンテスト
ユーザー hiromi_ayase
提出日時 2018-03-25 00:59:27
言語 Java
(openjdk 23)
結果
AC  
実行時間 804 ms / 2,000 ms
コード長 4,197 bytes
コンパイル時間 2,554 ms
コンパイル使用メモリ 81,892 KB
実行使用メモリ 40,368 KB
最終ジャッジ日時 2024-06-25 03:24:34
合計ジャッジ時間 16,420 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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 * 4
other AC * 15
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 #
raw source code 

public class Main {
  private static void solve() {
    long n = nl();
    int k = ni();
    int mod = 1000000000 + 7;

    System.out.println(powerSums(n, k, mod)[k]);
    
  }
  public static int[] enumInvs(int n, int mod)
  {
      int[] inv = new int[n+1];
      inv[1] = 1;
      for(int i = 2;i <= n;i++){
          inv[i] = (int)(inv[mod%i]*(long)(mod-mod/i)%mod);
      }
      return inv;
  }
  public static long[] powerSums(long n, int K, int mod)
  {
      int[] invs = enumInvs(K+1, mod);
      final long BIG = 1L*mod*mod;
      n %= mod;
      long[] s = new long[K+1];
      long[] c = new long[K+2];
      c[0] = 1;
      for(int i = 0;i <= K;i++){
          for(int j = i+1;j >= 1;j--){
              c[j] += c[j-1];
              if(c[j] >= mod)c[j] -= mod;
          }
          
          s[i] = pow(n+1, i+1, mod)-1;
          for(int j = 0;j <= i-1;j++){
              s[i] -= s[j]*c[j];
              if(s[i] < -BIG)s[i] += BIG;
          }
          s[i] %= mod;
          if(s[i] < 0)s[i] += mod;
          
          s[i] = s[i] * invs[i+1] % mod;
      }
      return s;
  }
  public static long pow(long a, long n, long mod)
  {
      if(a >= mod)a %= mod;
      long ret = 1;
      int x = 63-Long.numberOfLeadingZeros(n);
      for(;x >= 0;x--){
          ret = mul(ret, ret, mod);
          if(n<<~x<0)ret = mul(ret, a, mod);
      }
      return ret;
  }
  public static long mul(long a, long b, long mod)
  {
      if(a >= mod || a < 0)a %= mod;
      if(a < 0)a += mod;
      if(b >= mod || b < 0)b %= mod;
      if(b < 0)b += mod;
      
      long ret = 0;
      int x = 63-Long.numberOfLeadingZeros(b);
      for(;x >= 0;x--){
          ret += ret;
          if(ret >= mod)ret -= mod;
          if(b<<~x<0){
              ret += a;
              if(ret >= mod)ret -= mod;
          }
      }
      return ret;
  }
  
  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}
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