BIT

struct BIT {int n;vector<int> tr, vis;int tag;BIT(int _n = 0) { tag = 1; if (_n) init(_n); }void init(int _n) {n = _n;tr.assign(n + 1, 0);vis.assign(n + 1, 0);tag = 1;}int lowbit(int x) { return x & (-x); }// O(1) 清空：通过 tag + vis 做懒清空void clear() { tag ++ ; }inline void touch(int i) {if (vis[i] != tag) {vis[i] = tag;tr[i] = 0;}}// 单点加 kvoid add(int x, int k) {for (int i = x; i <= n; i += lowbit(i)) {touch(i);tr[i] += k;}}// 前缀和 [1..x]int sumPrefix(int x) {int res = 0;for (int i = x; i; i -= lowbit(i)) {touch(i);res += tr[i];}return res;}// 区间和 [l..r]int sumRange(int l, int r) {if (l > r) return 0;return sumPrefix(r) - sumPrefix(l - 1);}// 求第一个使得前缀和 >= k 的位置（k >= 1，且总和足够）int kth(int k) {int pos = 0;int bit = 1LL << __lg(n);for (int pw = bit; pw; pw >>= 1) {int nxt = pos + pw;if (nxt <= n) {touch(nxt);if (tr[nxt] < k) {k -= tr[nxt];pos = nxt;}}}return pos + 1;}
};