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| 1 | +/** |
| 2 | + * @file FDUPC25P-F.cpp |
| 3 | + * @author Macesuted (i@macesuted.moe) |
| 4 | + * @date 2025-11-27 |
| 5 | + * |
| 6 | + * @copyright Copyright (c) 2025 |
| 7 | + * |
| 8 | + */ |
| 9 | + |
| 10 | +#include <bits/stdc++.h> |
| 11 | +using namespace std; |
| 12 | + |
| 13 | +#ifndef LOCAL |
| 14 | +#define endl '\n' |
| 15 | +#endif |
| 16 | + |
| 17 | +bool mem1; |
| 18 | + |
| 19 | +#define maxn 100000 |
| 20 | + |
| 21 | +vector<int> Cs[maxn]; |
| 22 | + |
| 23 | +void solve(void) { |
| 24 | + int n, m, l, r; |
| 25 | + cin >> n >> m >> l >> r; |
| 26 | + |
| 27 | + int lim = 0; |
| 28 | + while (lim <= n && (int64_t)lim * (lim - 1) / 2 <= r) lim++; |
| 29 | + |
| 30 | + int ans = 0; |
| 31 | + |
| 32 | + // C(n, 0) |
| 33 | + if (l == 1) { |
| 34 | + if (lim <= 0) ans--; |
| 35 | + ans += max(0, n - lim + 1); |
| 36 | + ans += max(0, min(n, m) - lim + 1); |
| 37 | + } |
| 38 | + |
| 39 | + // C(n, 1) |
| 40 | + int xl = max(lim, l), xr = min(n, r); |
| 41 | + if (lim <= 2 && m >= 1) ans--; |
| 42 | + if (m >= 1) ans += max(0, xr - xl + 1); |
| 43 | + ans += max(0, min(xr, m + 1) - xl + 1); |
| 44 | + |
| 45 | + for (int i = 1; i < lim; i++) { |
| 46 | + int xl = lower_bound(Cs[i].begin(), Cs[i].end(), l) - Cs[i].begin(), |
| 47 | + xr = upper_bound(Cs[i].begin(), Cs[i].end(), r) - Cs[i].begin() - 1; |
| 48 | + ans += max(0, min(xr, m) - xl + 1); |
| 49 | + if (!(i & 1) && xr * 2 == i) xr--; |
| 50 | + tie(xl, xr) = make_pair(i - xr, i - xl); |
| 51 | + ans += max(0, min(xr, m) - xl + 1); |
| 52 | + } |
| 53 | + |
| 54 | + cout << ans << endl; |
| 55 | + |
| 56 | + return; |
| 57 | +} |
| 58 | + |
| 59 | +bool mem2; |
| 60 | + |
| 61 | +int main() { |
| 62 | + ios::sync_with_stdio(false), cin.tie(nullptr); |
| 63 | +#ifdef LOCAL |
| 64 | + cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl; |
| 65 | +#endif |
| 66 | + |
| 67 | + for (int i = 1; i < maxn; i++) { |
| 68 | + int64_t val = 1; |
| 69 | + for (int j = 0; j <= i - j && val <= 1e9; val = val * (i - j) / (j + 1), j++) Cs[i].push_back(val); |
| 70 | + } |
| 71 | + |
| 72 | + int _ = 1; |
| 73 | + cin >> _; |
| 74 | + while (_--) solve(); |
| 75 | + |
| 76 | +#ifdef LOCAL |
| 77 | + cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl; |
| 78 | +#endif |
| 79 | + return 0; |
| 80 | +} |
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