randomized_binary_search_tree.cpp

//
// Randomized Binary Search Tree (merge-split based)
//
// verified:
//   yukicoder No.649 ここでちょっと QK
//


#include <iostream>
using namespace std;


// RBST
typedef long long VAL;
const VAL SUM_UNITY = 0;
struct RBST {
	unsigned int randInt() {
		static unsigned int tx = 123456789, ty = 362436069, tz = 521288629, tw = 88675123;
		unsigned int tt = (tx ^ (tx << 11));
		tx = ty; ty = tz; tz = tw;
		return (tw = (tw ^ (tw >> 19)) ^ (tt ^ (tt >> 8)));
	}

	struct NODE {
		NODE *left, *right;
		VAL val;                        // the value of the node
		int size;                       // the size of the subtree 
		VAL sum;                        // the value-sum of the subtree

		NODE() : val(SUM_UNITY), size(1), sum(SUM_UNITY) {
			left = right = NULL;
		}

		NODE(VAL v) : val(v), size(1), sum(v) {
			left = right = NULL;
		}

		/* additional update */
		inline void update() {

		}

		/* additional lazy-propagation */
		inline void push() {

			/* ex: reverse */
			/*
			if (this->rev) {
			swap(this->left, this->right);
			if (this->left) this->left->rev ^= true;
			if (this->right) this->right->rev ^= true;
			this->rev = false;
			}
			*/
		}
	};


	///////////////////////
	// root
	///////////////////////

	NODE* root;
	RBST() : root(NULL) { }
	RBST(NODE* node) : root(node) { }


	///////////////////////
	// basic operations
	///////////////////////

	/* size */
	inline int size(NODE *node) {
		return !node ? 0 : node->size;
	}
	inline int size() {
		return this->size(this->root);
	}

	/* sum */
	inline VAL sum(NODE *node) {
		return !node ? SUM_UNITY : node->sum;
	}
	inline VAL sum() {
		return this->sum(this->root);
	}

	/* update, push */
	inline NODE* update(NODE *node) {
		node->size = size(node->left) + size(node->right) + 1;
		node->sum = sum(node->left) + sum(node->right) + node->val;
		node->update();
		return node;
	}

	inline void push(NODE *node) {
		if (!node) return;
		node->push();
	}

	/* lower_bound */
	inline int lowerBound(NODE *node, VAL val) {
		push(node);
		if (!node) return 0;
		if (val <= node->val) return lowerBound(node->left, val);
		else return size(node->left) + lowerBound(node->right, val) + 1;
	}
	inline int lowerBound(VAL val) {
		return this->lowerBound(this->root, val);
	}

	/* upper_bound */
	inline int upperBound(NODE *node, VAL val) {
		push(node);
		if (!node) return 0;
		if (val >= node->val) return size(node->left) + upperBound(node->right, val) + 1;
		else return upperBound(node->left, val);
	}
	inline int upperBound(VAL val) {
		return this->upperBound(this->root, val);
	}

	/* count */
	inline int count(VAL val) {
		return upperBound(val) - lowerBound(val);
	}

	/* get --- k: 0-index */
	inline VAL get(NODE *node, int k) {
		push(node);
		if (!node) return -1;
		if (k == size(node->left)) return node->val;
		if (k < size(node->left)) return get(node->left, k);
		else return get(node->right, k - size(node->left) - 1);
	}
	inline VAL get(int k) {
		return get(this->root, k);
	}


	///////////////////////
	// merge-split
	///////////////////////

	NODE* merge(NODE *left, NODE *right) {
		push(left);
		push(right);
		if (!left || !right) {
			if (left) return left;
			else return right;
		}
		if (randInt() % (left->size + right->size) < left->size) {
			left->right = merge(left->right, right);
			return update(left);
		}
		else {
			right->left = merge(left, right->left);
			return update(right);
		}
	}
	void merge(RBST add) {
		this->root = this->merge(this->root, add.root);
	}
	pair<NODE*, NODE*> split(NODE* node, int k) { // [0, k), [k, n)
		push(node);
		if (!node) return make_pair(node, node);
		if (k <= size(node->left)) {
			pair<NODE*, NODE*> sub = split(node->left, k);
			node->left = sub.second;
			return make_pair(sub.first, update(node));
		}
		else {
			pair<NODE*, NODE*> sub = split(node->right, k - size(node->left) - 1);
			node->right = sub.first;
			return make_pair(update(node), sub.second);
		}
	}
	RBST split(int k) {
		pair<NODE*, NODE*> sub = split(this->root, k);
		this->root = sub.first;
		return RBST(sub.second);
	}


	///////////////////////
	// insert-erase
	///////////////////////

	void insert(const VAL val) {
		pair<NODE*, NODE*> sub = this->split(this->root, this->lowerBound(val));
		this->root = this->merge(this->merge(sub.first, new NODE(val)), sub.second);
	}

	void erase(const VAL val) {
		if (!this->count(val)) return;
		pair<NODE*, NODE*> sub = this->split(this->root, this->lowerBound(val));
		this->root = this->merge(sub.first, this->split(sub.second, 1).second);
	}


	///////////////////////
	// debug
	///////////////////////

	void print(NODE *node) {
		if (!node) return;
		push(node);
		print(node->left);
		cout << node->val << " ";
		print(node->right);
	}
	void print() {
		cout << "{";
		print(this->root);
		cout << "}" << endl;
	}
};



//------------------------------//
// Examples
//------------------------------//

int main() {
	RBST S;
	int Q, K;
	cin >> Q >> K;
	for (int i = 0; i < Q; ++i) {
		int T;
		cin >> T;
		if (T == 1) {
			long long val;
			cin >> val;
			S.insert(val);
		}
		else {
			if (S.size() < K) {
				cout << -1 << endl;
				continue;
			}
			long long res = S.get(K - 1);
			cout << res << endl;
			S.erase(res);
		}
		//S.print();
	}
}