等差数列求和,找到中点 $k$,前半部分求和之后,分三种情况,前半部分和后半部分再利用等差数列求和来二分答案。
// Date: Fri Nov 24 21:14:51 2023
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;
const int INF = 0x3f3f3f3f, MOD = 1e9 + 7;
const double eps = 1e-8;
const int dir[8][2] = {
{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1},
};
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef pair<int, int> PII;
const ull Pr = 131;
#define For(i, a, b) for (int i = int(a); i < int(b); ++i)
#define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i)
#define For1(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i)
#define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i])
#define f1 first
#define f2 second
#define pb push_back
#define has(a, x) (a.find(x) != a.end())
#define nonempty(a) (!a.empty())
#define all(a) (a).begin(), (a).end()
#define SZ(a) int((a).size())
#ifdef _DEBUG
#define debug1(x) cout << #x " = " << x << endl;
#define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl;
#define debug3(x, y, z) \
cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl;
#else
#define debug1
#define debug2
#define debug3
#endif
int t;
int main(void) {
#ifdef _DEBUG
freopen("1612c.in", "r", stdin);
#endif
std::ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> t;
ll k, x;
while (t--) {
cin >> k >> x;
ll res = 0, top = (1 + k) * k / 2, l, r, mid, sum;
if (x == top) {
res = k;
} else if (x < top) {
l = 1, r = k;
while (l < r) {
mid = (l + r) / 2;
sum = mid * (1 + mid) / 2;
if (sum >= x)
r = mid;
else
l = mid + 1;
}
res = r;
} else {
res = k;
x -= top;
l = 1, r = k - 1;
while (l < r) {
mid = (l + r) / 2;
sum = k * mid - (mid + 1) * mid / 2;
if (sum >= x)
r = mid;
else
l = mid + 1;
}
sum = k * r - (r + 1) * r / 2;
if (sum < x) {
res = 2 * k - 1;
} else {
res += r;
}
}
cout << res << '\n';
}
return 0;
}