結果

問題 No.2127 Mod, Sum, Sum, Mod
コンテスト
ユーザー hiromi_ayase
提出日時 2022-11-19 18:53:16
言語 Java
(openjdk 23)
結果
AC  
実行時間 289 ms / 2,000 ms
コード長 4,090 bytes
コンパイル時間 2,488 ms
コンパイル使用メモリ 89,580 KB
実行使用メモリ 53,064 KB
最終ジャッジ日時 2024-09-21 00:41:56
合計ジャッジ時間 6,798 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 * 3
other AC * 27
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ソースコード

diff #
raw source code 

import java.util.*;

@SuppressWarnings("unused")
public class Main {

  private static void solve() {
    long n = nl();
    long m = nl();

    System.out.println(solve(n, m));

  }

  static int mod = 998244353;

  private static long solve(long n, long m) {
    long sum = n * (n + 1) / 2;

    long ret = 0;

    for (long j = 1; j <= m;) {

      long left = j;
      long right = m + 1;
      while (Math.abs(left - right) > 1) {
        long k = (left + right) / 2;
        if (n / k == n / j) {
          left = k;
        } else {
          right = k;
        }
      }

      long nj = right;
      long z = n / j;
      // [j, nj)
      // (j^2 - j)/2
      //
      {
        long j0 = nj - j;
        long j2 = 0;
        j2 += nj * (nj - 1) % mod * (2 * nj - 1) % mod;
        j2 += mod - j * (j - 1) % mod * (2 * j - 1) % mod;
        j2 %= mod;
        j2 *= inv(6, mod);
        j2 %= mod;

        long j1 = 0;
        j1 += nj * (nj - 1) / 2 % mod;
        j1 += (mod - j * (j - 1) / 2 % mod) % mod;
        j1 %= mod;

        // z * (j2 - j1) / 2
        ret += z * (j2 - j1 + mod) % mod * inv(2, mod) % mod;

        // x = n % j = n - z*j
        // ret += x * (x + 1) / 2
        // = (n - z*j) * (n - z * j + 1) / 2
        // = (n*(n+1) + z^2 * j^2 + z*(2n+1)*j) / 2
        ret += n * (n + 1) / 2 % mod * j0 % mod;
        ret += (z * z % mod * j2 % mod + mod - z * (2 * n + 1) % mod * j1 % mod) % mod * inv(2, mod) % mod;
        ret %= mod;
      }

      j = nj;
    }

    return ret;
  }

  public static long inv(long a, int p) {
    long ret = 1;
    long mul = a;
    for (long n = p - 2; n > 0; n >>>= 1) {
      if ((n & 1) == 1)
        ret = ret * mul % p;
      mul = mul * mul % p;
    }
    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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