#978823 (Go) No.2065 Sum of Min

提出ソース
結果

問題	No.2065 Sum of Min
ユーザー	草苺奶昔
提出日時	2024-05-03 17:11:32
言語	Go (1.22.1)
結果	AC
実行時間	432 ms / 2,000 ms
コード長	18,180 bytes
コンパイル時間	12,616 ms
コンパイル使用メモリ	224,016 KB
実行使用メモリ	26,364 KB
最終ジャッジ日時	2024-05-03 17:12:02
合計ジャッジ時間	20,951 ms
ジャッジサーバーID （参考情報）	judge2 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,816 KB
testcase_01	AC	1 ms 6,944 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	1 ms 6,944 KB
testcase_04	AC	276 ms 22,888 KB
testcase_05	AC	283 ms 22,656 KB
testcase_06	AC	169 ms 14,088 KB
testcase_07	AC	186 ms 12,200 KB
testcase_08	AC	214 ms 12,204 KB
testcase_09	AC	404 ms 26,364 KB
testcase_10	AC	342 ms 25,984 KB
testcase_11	AC	339 ms 25,984 KB
testcase_12	AC	432 ms 26,112 KB
testcase_13	AC	415 ms 26,112 KB
testcase_14	AC	416 ms 26,112 KB
testcase_15	AC	425 ms 26,112 KB
testcase_16	AC	420 ms 26,112 KB
testcase_17	AC	418 ms 26,112 KB
testcase_18	AC	431 ms 26,112 KB
testcase_19	AC	426 ms 26,112 KB
testcase_20	AC	423 ms 26,112 KB
testcase_21	AC	427 ms 26,112 KB
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ソースコード

raw source code
// 维护区间贡献的 Wavelet Matrix
// !注意查询区间贡献时, 异或无效
//
// api:
//  !RangeCountAndSum(start, end, a, b, xor) - 区间 [start, end) 中值在 [a, b) 之间的数的个数和这些数的和.
//  !KthValueAndSum(start, end, k, xor) - 区间 [start, end) 中第 k 小的数和前 k 小的数的和.
//
//  Kth(start, end, k, xor) - 区间 [start, end) 中第 k 小的数.
//  Median(start, end, upper, xor) - 区间 [start, end) 中的中位数.
//  Floor(start, end, x, xor) - 区间 [start, end) 中值小于等于 x 的最大值
//  Ceil(start, end, x, xor) - 区间 [start, end) 中值大于等于 x 的最小值
//
//  SumAll(start, end) - 区间 [start, end) 中所有数的和.
//  SumRange(start, end, a, b, xor) - 区间 [start, end) 中值在 [a, b) 之间的数的和.
//  SumSlice(start, end, k1, k2, xor) - 区间 [start, end) 中第 k1 到第 k2 小的数的和.
//
//  MaxRight(start, end, xor, check) - 返回使得 check(count,prefixSum) 为 true 的最大(count,prefixSum), 其中prefixSum为[0,val)内的数的和.

package main

import (
	"bufio"
	"fmt"
	"math/bits"
	"os"
	"sort"
)

func main() {
	// demo()
	// 区间最短距离和()
	// abc281_e()

	// yuki919()
	// yuki1332()
	yuki2065()
}

func demo() {
	nums := []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
	wm := NewWaveletMatrixWithSum(nums, nums, -1, true)
	fmt.Println(wm.RangeCountAndSum(0, 3, 3, 7, 0))
	fmt.Println(wm.KthValueAndSum(1, 5, 0, 0))
	nums = []int{1, 2, 3, 4, 5}
	wm = NewWaveletMatrixWithSum(nums, nums, -1, false)
	fmt.Println(wm.KthValueAndSum(0, 5, 2, 0))
	fmt.Println(wm.KthValueAndSum(0, 6, 5, 0))
	fmt.Println(wm.SumAll(0, 4))

	fmt.Println(wm.Floor(0, 5, 4, 0))
	fmt.Println(wm.Kth(0, 5, 1, 0))
}

func abc281_e() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()
	var n, m, k int32
	fmt.Fscan(in, &n, &m, &k)
	nums := make([]int, n)
	for i := range nums {
		fmt.Fscan(in, &nums[i])
	}
	wm := NewWaveletMatrixWithSum(nums, nums, -1, false)
	for i := int32(0); i < n-m+1; i++ {
		_, res := wm.KthValueAndSum(i, i+m, k, 0)
		fmt.Fprintln(out, res)
	}
}

// 子数组所有数到中位数的距离和(区间中位数距离和)
// https://yukicoder.me/problems/no/924
// n,q<=2e5
// -1e9 <= nums[i] <= 1e9
// 给定n个查询[l,r]
// !求区间[l,r]中位数到区间[l,r]中每个数的距离之和
// !也就求函数 f(x)= ∑|nums[i]-x| (l<=i<=right) 的最小值
// !区间中位数
func 区间最短距离和() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n, q int
	fmt.Fscan(in, &n, &q)
	OFFSET := int(1e9 + 10)
	nums := make([]int, n)
	for i := range nums {
		fmt.Fscan(in, &nums[i])
		nums[i] += OFFSET
	}

	wm := NewWaveletMatrixWithSum(nums, nums, -1, false)
	for i := 0; i < q; i++ {
		var start, end int32
		fmt.Fscan(in, &start, &end)
		start--

		n := end - start
		lowerCount := n / 2
		ceilCount := n - lowerCount
		mid, lowerSum := wm.KthValueAndSum(start, end, lowerCount, 0)
		allSum := wm.SumAll(start, end)
		ceilSum := allSum - lowerSum

		res := 0
		res += mid*int(lowerCount) - lowerSum
		res += ceilSum - mid*int(ceilCount)
		fmt.Fprintln(out, res)
	}
}

// No.919 You Are A Project Manager (区间中位数+前后缀分解)
// https://yukicoder.me/problems/no/919
// 给定一个数组nums，需要分为若干组.
// 初始时选择分组大小k，每次分组需要从最左边或最右边取k个数分为一组，
// 每个组的的得分为k*组内中位数(这里的中位数向下).
// 求最大化总得分.
//
// n<=1e4,-1e9<=nums[i]<1e9
func yuki919() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n int32
	fmt.Fscan(in, &n)
	nums := make([]int, n)
	for i := range nums {
		fmt.Fscan(in, &nums[i])
	}

	wm := NewWaveletMatrixWithSum(nums, nil, -1, true)
	median := func(start, end int32) int {
		return wm.Median(start, end, false, 0)
	}

	res := -INF
	for size := int32(1); size <= n; size++ {
		count := n / size
		leftScore, rightScore := make([]int, count), make([]int, count)
		for i := int32(0); i < count; i++ {
			leftScore[i] = median(i*size, i*size+size)
			rightScore[i] = median(n-i*size-size, n-i*size)
		}
		leftPresum, rightPresum := make([]int, count+1), make([]int, count+1)
		for i := int32(0); i < count; i++ {
			leftPresum[i+1] = leftPresum[i] + leftScore[i]
			rightPresum[i+1] = rightPresum[i] + rightScore[i]
		}
		for i := int32(0); i < count; i++ {
			leftPresum[i+1] = max(leftPresum[i+1], leftPresum[i])
			rightPresum[i+1] = max(rightPresum[i+1], rightPresum[i])
		}
		for i := int32(0); i <= count; i++ {
			res = max(res, int(size)*(leftPresum[i]+rightPresum[count-i]))
		}
	}

	fmt.Fprintln(out, res)

}

// No.1332 Range Nearest Query
// https://yukicoder.me/problems/no/1332
// 区间最近值(无序数组区间前驱后继)查询
// !对每个查询[left,right,x],输出左闭右开区间内的数到给定数x的最小距离
// n<=3e5 q<=1e5 nums[i]<=1e9
func yuki1332() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n int
	fmt.Fscan(in, &n)
	nums := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Fscan(in, &nums[i])
	}

	M := NewWaveletMatrixWithSum(nums, nil, -1, true)
	var q int
	fmt.Fscan(in, &q)
	for i := 0; i < q; i++ {
		var start, end int32
		var x int
		fmt.Fscan(in, &start, &end, &x)
		start--
		res := INF
		floor := M.Floor(start, end, x, 0) // 小于等于x的最大值
		if floor != -INF {
			res = min(res, abs(floor-x))
		}
		ceiling := M.Ceil(start, end, x, 0) // 大于等于x的最小值
		if ceiling != INF {
			res = min(res, abs(ceiling-x))
		}
		fmt.Fprintln(out, res)
	}
}

// No.2065 Sum of Min (区间chmin之和)
// https://yukicoder.me/problems/no/2065
// 小于x数的和+(end-start-小于x数的个数)*x
func yuki2065() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n, q int32
	fmt.Fscan(in, &n, &q)
	nums := make([]int, n)
	for i := range nums {
		fmt.Fscan(in, &nums[i])
	}

	M := NewWaveletMatrixWithSum(nums, nums, -1, true)
	for i := int32(0); i < q; i++ {
		var start, end int32
		var x int
		fmt.Fscan(in, &start, &end, &x)
		start--
		lessCount, lessSum := M.RangeCountAndSum(start, end, 0, x, 0) // 小于x的数的个数
		res := lessSum + int((end-start-lessCount))*x
		fmt.Fprintln(out, res)
	}
}

const INF WmValue = 1e18

type WmValue = int
type WmSum = int

func (*WaveletMatrixWithSum) e() WmSum            { return 0 }
func (*WaveletMatrixWithSum) op(a, b WmSum) WmSum { return a + b }
func (*WaveletMatrixWithSum) inv(a WmSum) WmSum   { return -a }

type WaveletMatrixWithSum struct {
	n, log   int32
	setLog   bool
	compress bool
	useSum   bool
	mid      []int32
	bv       []*BitVector
	key      []WmValue
	presum   [][]WmSum
}

// nums: 数组元素.
// sumData: 和数据，nil表示不需要和数据.
// log: 如果需要支持异或查询则需要传入log，-1表示默认.
// compress: 是否对nums进行离散化(值域较大(1e9)时可以离散化加速).
func NewWaveletMatrixWithSum(nums []WmValue, sumData []WmSum, log int32, compress bool) *WaveletMatrixWithSum {
	wm := &WaveletMatrixWithSum{}
	wm.build(nums, sumData, log, compress)
	return wm
}

func (wm *WaveletMatrixWithSum) build(nums []WmValue, sumData []WmSum, log int32, compress bool) {
	numsCopy := append(nums[:0:0], nums...)
	sumDataCopy := append(sumData[:0:0], sumData...)

	wm.n = int32(len(numsCopy))
	wm.log = log
	wm.setLog = log != -1
	wm.compress = compress
	wm.useSum = len(sumData) > 0
	if wm.n == 0 {
		wm.log = 0
		wm.presum = [][]WmSum{{wm.e()}}
		return
	}

	if compress {
		if wm.setLog {
			panic("compress and log should not be set at the same time")
		}
		wm.key = make([]WmValue, 0, wm.n)
		order := wm._argSort(numsCopy)
		for _, i := range order {
			if len(wm.key) == 0 || wm.key[len(wm.key)-1] != numsCopy[i] {
				wm.key = append(wm.key, numsCopy[i])
			}
			numsCopy[i] = WmValue(len(wm.key) - 1)
		}
		wm.key = wm.key[:len(wm.key):len(wm.key)]
	}
	if wm.log == -1 {
		tmp := wm._maxs(numsCopy)
		if tmp < 1 {
			tmp = 1
		}
		wm.log = int32(bits.Len(uint(tmp)))
	}
	wm.mid = make([]int32, wm.log)
	wm.bv = make([]*BitVector, wm.log)
	for i := range wm.bv {
		wm.bv[i] = NewBitVector(wm.n)
	}
	if wm.useSum {
		wm.presum = make([][]WmSum, 1+wm.log)
		for i := range wm.presum {
			sums := make([]WmSum, wm.n+1)
			for j := range sums {
				sums[j] = wm.e()
			}
			wm.presum[i] = sums
		}
	}
	if len(sumDataCopy) == 0 {
		sumDataCopy = make([]WmSum, len(numsCopy))
	}

	A, S := numsCopy, sumDataCopy
	A0, A1 := make([]WmValue, wm.n), make([]WmValue, wm.n)
	S0, S1 := make([]WmSum, wm.n), make([]WmSum, wm.n)
	for d := wm.log - 1; d >= -1; d-- {
		p0, p1 := int32(0), int32(0)
		if wm.useSum {
			tmp := wm.presum[d+1]
			for i := int32(0); i < wm.n; i++ {
				tmp[i+1] = wm.op(tmp[i], S[i])
			}
		}
		if d == -1 {
			break
		}
		for i := int32(0); i < wm.n; i++ {
			f := (A[i] >> d & 1) == 1
			if !f {
				if wm.useSum {
					S0[p0] = S[i]
				}
				A0[p0] = A[i]
				p0++
			} else {
				if wm.useSum {
					S1[p1] = S[i]
				}
				wm.bv[d].Set(i)
				A1[p1] = A[i]
				p1++
			}
		}
		wm.mid[d] = p0
		wm.bv[d].Build()
		A, A0 = A0, A
		S, S0 = S0, S
		for i := int32(0); i < p1; i++ {
			A[p0+i] = A1[i]
			S[p0+i] = S1[i]
		}
	}
}

// 返回区间 [start, end) 中 值在 [a, b) 中的元素个数以及这些元素的和.
func (wm *WaveletMatrixWithSum) RangeCountAndSum(start, end int32, a, b WmValue, xorValue WmValue) (int32, WmSum) {
	if xorValue != 0 {
		if !wm.setLog {
			panic("log should be set when xor is used")
		}
	}
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end || a >= b {
		return 0, wm.e()
	}
	if wm.compress {
		a = wm._lowerBound(wm.key, a)
		b = wm._lowerBound(wm.key, b)
	}
	count, sum := int32(0), wm.e()
	var dfs func(d, l, r int32, lx, rx WmValue)
	dfs = func(d, l, r int32, lx, rx WmValue) {
		if rx <= a || b <= lx {
			return
		}
		if a <= lx && rx <= b {
			count += r - l
			if wm.useSum {
				sum = wm.op(sum, wm._get(d, l, r))
			}
			return
		}
		d--
		mx := (lx + rx) >> 1
		l0, r0 := wm.bv[d].Rank(l, false), wm.bv[d].Rank(r, false)
		l1, r1 := l+wm.mid[d]-l0, r+wm.mid[d]-r0
		if xorValue>>d&1 == 1 {
			l0, l1 = l1, l0
			r0, r1 = r1, r0
		}
		dfs(d, l0, r0, lx, mx)
		dfs(d, l1, r1, mx, rx)
	}
	dfs(wm.log, start, end, 0, 1<<wm.log)
	return count, sum
}

// 返回区间 [start, end) 中的 (第k小的元素, 前k个元素(不包括第k小的元素) 的 op 的结果).
// 如果k >= end-start, 返回 (-1, 区间 op 的结果).
func (wm *WaveletMatrixWithSum) KthValueAndSum(start, end, k int32, xorVal WmValue) (WmValue, WmSum) {
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end {
		return -1, wm.e()
	}
	if k >= end-start {
		return -1, wm.SumAll(start, end)
	}
	if xorVal != 0 {
		if !wm.setLog {
			panic("log should be set when xor is used")
		}
	}

	sum, val := wm.e(), WmValue(0)
	for d := wm.log - 1; d >= 0; d-- {
		l0, r0 := wm.bv[d].Rank(start, false), wm.bv[d].Rank(end, false)
		l1, r1 := start+wm.mid[d]-l0, end+wm.mid[d]-r0
		if (xorVal>>d)&1 == 1 {
			l0, l1 = l1, l0
			r0, r1 = r1, r0
		}
		if k < r0-l0 {
			start, end = l0, r0
		} else {
			k -= r0 - l0
			val |= 1 << d
			start, end = l1, r1
			if wm.useSum {
				sum = wm.op(sum, wm._get(d, l0, r0))
			}
		}
	}
	if wm.useSum {
		sum = wm.op(sum, wm._get(0, start, start+k))
	}
	if wm.compress {
		val = wm.key[val]
	}
	return val, sum
}

// [start, end)区间内第k(k>=0)小的元素.
func (wm *WaveletMatrixWithSum) Kth(start, end, k int32, xorVal WmValue) WmValue {
	if k < 0 {
		k = 0
	}
	if n := end - start - 1; k > n {
		k = n
	}
	v, _ := wm.KthValueAndSum(start, end, k, xorVal)
	return v
}

// upper: 向上取中位数还是向下取中位数.
func (wm *WaveletMatrixWithSum) Median(start, end int32, upper bool, xorVal WmValue) WmValue {
	n := end - start
	var k int32
	if upper {
		k = n >> 1
	} else {
		k = (n - 1) >> 1
	}
	return wm.Kth(start, end, k, xorVal)
}

// [start, end) 中小于等于 x 的数中最大的数.
//
//	如果不存在则返回-INF.
func (wm *WaveletMatrixWithSum) Floor(start, end int32, x WmValue, xor WmValue) WmValue {
	if xor != 0 {
		if !wm.setLog {
			panic("log should be set when xor is used")
		}
	}
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end {
		return -INF
	}
	res := -INF
	x++
	if wm.compress {
		x = wm._lowerBound(wm.key, x)
	}
	var dfs func(d, l, r int32, lx, rx WmValue)
	dfs = func(d, l, r int32, lx, rx WmValue) {
		if rx-1 <= res || l == r || x <= lx {
			return
		}
		if d == 0 {
			res = max(res, lx)
			return
		}
		d--
		mx := (lx + rx) >> 1
		l0, r0 := wm.bv[d].Rank(l, false), wm.bv[d].Rank(r, false)
		l1, r1 := l+wm.mid[d]-l0, r+wm.mid[d]-r0
		if xor>>d&1 == 1 {
			l0, l1 = l1, l0
			r0, r1 = r1, r0
		}
		dfs(d, l1, r1, mx, rx)
		dfs(d, l0, r0, lx, mx)
	}
	dfs(wm.log, start, end, 0, 1<<wm.log)
	if wm.compress && res != -INF {
		res = wm.key[res]
	}
	return res
}

// [start, end) 中大于等于 x 的数中最小的数
//
//	如果不存在则返回INF
func (wm *WaveletMatrixWithSum) Ceil(start, end int32, x WmValue, xor WmValue) int {
	if xor != 0 {
		if !wm.setLog {
			panic("log should be set when xor is used")
		}
	}
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end {
		return INF
	}
	res := INF
	if wm.compress {
		x = wm._lowerBound(wm.key, x)
	}
	var dfs func(d, l, r int32, lx, rx WmValue)
	dfs = func(d, l, r int32, lx, rx WmValue) {
		if res <= lx || l == r || x <= lx {
			return
		}
		if d == 0 {
			res = min(res, rx)
			return
		}
		d--
		mx := (lx + rx) >> 1
		l0, r0 := wm.bv[d].Rank(l, false), wm.bv[d].Rank(r, false)
		l1, r1 := l+wm.mid[d]-l0, r+wm.mid[d]-r0
		if xor>>d&1 == 1 {
			l0, l1 = l1, l0
			r0, r1 = r1, r0
		}
		dfs(d, l0, r0, lx, mx)
		dfs(d, l1, r1, mx, rx)
	}
	dfs(wm.log, start, end, 0, 1<<wm.log)
	if wm.compress && res < INF {
		res = wm.key[res]
	}
	return res
}

// 返回区间 [start, end) 中 范围在 [a, b) 中的元素的和.
func (wm *WaveletMatrixWithSum) SumRange(start, end int32, a, b WmValue, xorVal WmValue) WmSum {
	if !wm.useSum {
		panic("sum data must be provided")
	}
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end || a >= b {
		return wm.e()
	}
	_, sum := wm.RangeCountAndSum(start, end, a, b, xorVal)
	return sum
}

// 返回区间 [start, end) 中 排名在 [k1, k2) 中的元素的和.
func (wm *WaveletMatrixWithSum) SumSlice(start, end, k1, k2 int32, xorVal WmValue) WmSum {
	if !wm.useSum {
		panic("sum data must be provided")
	}
	if k1 < 0 {
		k1 = 0
	}
	if k2 > end-start {
		k2 = end - start
	}
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end || k1 >= k2 {
		return wm.e()
	}
	_, sum1 := wm.KthValueAndSum(start, end, k1, xorVal)
	_, sum2 := wm.KthValueAndSum(start, end, k2, xorVal)
	return wm.op(sum2, wm.inv(sum1))
}

func (wm *WaveletMatrixWithSum) SumAll(start, end int32) WmSum {
	if start < 0 {
		start = 0
	}
	if end > wm.n {
		end = wm.n
	}
	if start >= end {
		return wm.e()
	}
	return wm._get(wm.log, start, end)
}

// 使得predicate(count, sum)为true的最大的(count, sum).
func (wm *WaveletMatrixWithSum) MaxRight(predicate func(int32, WmSum) bool, start, end int32, xorVal WmValue) (int32, WmSum) {
	if xorVal != 0 {
		if !wm.setLog {
			panic("log should be set when xor is used")
		}
	}
	if start >= end {
		return 0, wm.e()
	}
	if s := wm._get(wm.log, start, end); predicate(end-start, s) {
		return end - start, s
	}
	count, sum := int32(0), wm.e()
	for d := wm.log - 1; d >= 0; d-- {
		l0, r0 := wm.bv[d].Rank(start, false), wm.bv[d].Rank(end, false)
		l1, r1 := start+wm.mid[d]-l0, end+wm.mid[d]-r0
		if xorVal>>d&1 == 1 {
			l0, l1 = l1, l0
			r0, r1 = r1, r0
		}
		if s := wm.op(sum, wm._get(d, l0, r0)); predicate(count+r0-l0, s) {
			count += r0 - l0
			sum = s
			start, end = l1, r1
		} else {
			start, end = l0, r0
		}
	}
	k := wm._binarySearch(func(k int32) bool {
		return predicate(count+k, wm.op(sum, wm._get(0, start, start+k)))
	}, 0, end-start)
	count += k
	sum = wm.op(sum, wm._get(0, start, start+k))
	return count, sum
}

func (wm *WaveletMatrixWithSum) _get(d, l, r int32) WmSum {
	if wm.useSum {
		return wm.op(wm.presum[d][r], wm.inv(wm.presum[d][l]))
	}
	return wm.e()
}

func (wm *WaveletMatrixWithSum) _argSort(nums []WmValue) []int32 {
	order := make([]int32, len(nums))
	for i := range order {
		order[i] = int32(i)
	}
	sort.Slice(order, func(i, j int) bool { return nums[order[i]] < nums[order[j]] })
	return order
}

func (wm *WaveletMatrixWithSum) _maxs(nums []WmValue) WmValue {
	res := nums[0]
	for _, v := range nums {
		if v > res {
			res = v
		}
	}
	return res
}

func (wm *WaveletMatrixWithSum) _lowerBound(nums []WmValue, target WmValue) WmValue {
	left, right := int32(0), int32(len(nums)-1)
	for left <= right {
		mid := (left + right) >> 1
		if nums[mid] < target {
			left = mid + 1
		} else {
			right = mid - 1
		}
	}
	return WmValue(left)
}

func (wm *WaveletMatrixWithSum) _binarySearch(f func(int32) bool, ok, ng int32) int32 {
	for abs32(ok-ng) > 1 {
		x := (ok + ng) >> 1
		if f(x) {
			ok = x
		} else {
			ng = x
		}
	}
	return ok
}

type BitVector struct {
	bits   []uint64
	preSum []int32
}

func NewBitVector(n int32) *BitVector {
	return &BitVector{bits: make([]uint64, n>>6+1), preSum: make([]int32, n>>6+1)}
}

func (bv *BitVector) Set(i int32) {
	bv.bits[i>>6] |= 1 << (i & 63)
}

func (bv *BitVector) Build() {
	for i := 0; i < len(bv.bits)-1; i++ {
		bv.preSum[i+1] = bv.preSum[i] + int32(bits.OnesCount64(bv.bits[i]))
	}
}

func (bv *BitVector) Rank(k int32, f bool) int32 {
	m, s := bv.bits[k>>6], bv.preSum[k>>6]
	res := s + int32(bits.OnesCount64(m&((1<<(k&63))-1)))
	if f {
		return res
	}
	return k - res
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func abs32(x int32) int32 {
	if x < 0 {
		return -x
	}
	return x
}

func min32(a, b int32) int32 {
	if a < b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}