E. Klee's SUPER DUPER LARGE Array!!!

# Klee's SUPER DUPER LARGE Array!!!

题面翻译

题目大意

你将得到一个长度为 的序列 ，请求出 的值，其中

输入格式

本题存在多组测试数据。第一行为一个正整数 （），表示数据组数。对于每组数据分别给出用空格隔开的两个整数 与 （）。

输出格式

对于每组数据，输出一行一个整数 。

题目描述

Klee has an array of length containing integers in that order. Klee wants to choose an index ( ) such that is minimized. Note that for an arbitrary integer , represents the absolute value of .

Output the minimum possible value of .

输入格式

The first line contains ( ) — the number of test cases.

Each test case contains two integers and ( ) — the length of the array and the starting element of the array.

输出格式

For each test case, output the minimum value of on a new line.

样例 #1

样例输入 #1

4
2 2
7 2
5 3
1000000000 1000000000

样例输出 #1

1
5
1
347369930

提示

In the first sample, . When is chosen, . It can be shown this is the minimum possible value of .

In the third sample, . When is chosen, . It can be shown this is the minimum possible value of .

题解

#include <bits/stdc++.h>
#define int long long
using namespace std;
int f(int x,int b,int c){
    return (int)abs(x*x+b*x-c);
}
signed main(){
    int t,n,k;
    cin>>t;
    while(t--){
        cin>>n>>k;
        int b=2*k-1,c=(n*(2*k+n-1)/2);
        double delta=1.0*b*b+4.0*c;
        double x=1.0*(sqrt(delta)-1.0*b)/2.0;
        int nx=(int)x;
        cout<<min(f(nx,b,c),f(nx+1,b,c))<<endl;
    }
    return 0;
}