結果

問題 No.1918 Simple Math ?
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-04-29 21:37:48
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 1,082 ms / 2,000 ms
コード長 4,854 bytes
コンパイル時間 1,536 ms
コンパイル使用メモリ 153,628 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-22 15:00:23
合計ジャッジ時間 14,730 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
sample AC * 1
other AC * 33
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 # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }

struct ModInt(uint M_) {
  import std.conv : to;
  alias M = M_;
  uint x;
  this(ModInt a) { x = a.x; }
  this(uint x_) { x = x_ % M; }
  this(ulong x_) { x = x_ % M; }
  this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
  this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
  ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op, T)(T a) {
    static if (is(T == ModInt)) {
      static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
      else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
      else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
      else static if (op == "/") { this *= a.inv(); }
      else static assert(false);
      return this;
    } else static if (op == "^^") {
      if (a < 0) return this = inv()^^(-a);
      ModInt b = this, c = 1U;
      for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
      return this = c;
    } else {
      return mixin("this " ~ op ~ "= ModInt(a)");
    }
  }
  ModInt inv() const {
    uint a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
    assert(a == 1); return ModInt(y);
  }
  ModInt opUnary(string op)() const {
    static if (op == "+") { return this; }
    else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
    else static assert(false);
  }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  bool opCast(T: bool)() const { return (x != 0U); }
  string toString() const { return x.to!string; }
}

enum MO = 10^^9 + 7;
alias Mint = ModInt!MO;


// floor(a / b)
Int divFloor(Int)(Int a, Int b) {
  return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}

// ceil(a / b)
Int divCeil(Int)(Int a, Int b) {
  return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}

// floor(sqrt(a))
long floorSqrt(long a) {
  import core.bitop : bsr;
  import std.algorithm : min;
  long b = a, x = 0, y = 0;
  for (int e = bsr(a) & ~1; e >= 0; e -= 2) {
    x <<= 1;
    y <<= 1;
    if (b >= (y | 1) << e) {
      b -= (y | 1) << e;
      x |= 1;
      y += 2;
    }
  }
  return x;
}


void main() {
  try {
    for (; ; ) {
      const numCases = readInt;
      foreach (caseId; 0 .. numCases) {
        const A = readLong;
        const N = readLong;
        
        const denom = Mint(6 * A).inv;
        
        const km = floorSqrt(A * N);
        Mint ans;
        ans += Mint(N - divFloor(km^^2 - 1, A)) * Mint(km);
        debug {
          writeln("km = ", km);
          writeln("ans = ", ans);
        }
        
        foreach (r; 0 .. A) {
          // 0 < A q + r <= km - 1
          const long lb = divFloor(0 - r, A);
          const long ub = divFloor(km - 1 - r, A);
          if (lb < ub) {
            // k^2 - 1 < i <= k^2 + 2 k
            const x = (r^^2 - 1 + A) % A;
            const y = (r^^2 + 2 * r) % A;
            
            Mint calc(Mint m) {
              return (1+m) * (2*A*A*m*(1+2*m) + 6*r*(1+2*r+x-y) + 3*A*m*(1+4*r+x-y)) * denom;
            }
            debug {
              if (A <= 10) {
                writeln(r, " ", [lb, ub], " ", [x, y], " ", [calc(Mint(lb)), calc(Mint(ub))]);
              }
            }
            ans += calc(Mint(ub));
            ans -= calc(Mint(lb));
          }
        }
        writeln(ans);
      }
    }
  } catch (EOFException e) {
  }
}
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