Problem:
Score : 400 points

Problem Statement

There are N one-off jobs available. If you take the i-th job and complete it, you will earn the reward of B_i after A_i days from the day you do it.

You can take and complete at most one of these jobs in a day.

However, you cannot retake a job that you have already done.

Find the maximum total reward that you can earn no later than M days from today.

You can already start working today.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i \leq 10^5

1 \leq B_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Print the maximum total reward that you can earn no later than M days from today.

Sample Input 1

3 4
4 3
4 1
2 2

Sample Output 1

5

You can earn the total reward of 5 by taking the jobs as follows:

Take and complete the first job today. You will earn the reward of 3 after four days from today.

Take and complete the third job tomorrow. You will earn the reward of 2 after two days from tomorrow, that is, after three days from today.

Sample Input 2

5 3
1 2
1 3
1 4
2 1
2 3

Sample Output 2

10

Sample Input 3

1 1
2 1

Sample Output 3

0

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"bytes"
	"container/heap"
	"fmt"
	"io"
	"os"
	"reflect"
	"strconv"
	"unsafe"
)

// -----------------------------------------------------------------------------

// IO helper functions

// Returns next token from input.  It must be initialized by SetInput()
// before the first call.
var nextToken func() ([]byte, error)
var nextLine func() ([]byte, error)

// Holds a buffer for output.  It must be initialized by SetOutput().
// All IO fucntions (read*() and [e]print*()) should write to OutputWriter
// instead of this.
var OutputBuffer *bufio.Writer

// Holds an io.Writer.  It must be initialized by SetOutput()
var OutputWriter io.Writer

// Set IO functions for interactive input/output.
func SetInteractive(w io.Writer, r io.Reader) {
	SetUnbefferedInput(r)
	OutputBuffer = nil
	OutputWriter = w
}

// Setup OutputBuffer and OutputWriter.
func SetOutput(w io.Writer) {
	OutputBuffer = bufio.NewWriter(w)
	OutputWriter = OutputBuffer
}

// Flushes OutputBuffer
func Flush() {
	if OutputBuffer != nil {
		OutputBuffer.Flush()
	}
}

// Returns true if c is a white space
func IsSpace(c byte) bool {
	switch c {
	case '\t', '\n', '\v', '\f', '\r', ' ':
		return true
	}
	return false
}

func IsNewLine(c byte) bool {
	switch c {
	case '\n', '\r':
		return true
	}
	return false
}

// Setup nextToken with input buffer.
func SetInput(r io.Reader) {
	buf := new(bytes.Buffer)
	var b []byte

	var i int
	rest := func() ([]byte, error) {
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		return b[j:i], nil
	}
	initial := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextToken = rest
		return rest()
	}
	nextToken = initial

	restLn := func() ([]byte, error) {
		for i < len(b) && IsNewLine(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsNewLine(b[i]) {
			i++
		}
		return b[j:i], nil
	}

	initialLn := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextLine = restLn
		return restLn()
	}
	nextLine = initialLn
}

// Setup nextToken without input buffer.
func SetUnbefferedInput(r io.Reader) {
	buf := bufio.NewReader(r)
	var b []byte

	var i int
	nextToken = func() ([]byte, error) {
		var err error
		if i == len(b) {
			b, err = buf.ReadBytes('\n')
			if err != nil {
				return nil, err
			}
			i = 0
			j := len(b) - 1
			for 0 <= j && IsSpace(b[j]) {
				j--
			}
			b = b[0 : j+1]
		}
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		if i == j {
			return nil, io.ErrUnexpectedEOF
		}
		return b[j:i], nil
	}
}

// -----------------------------------------------------------------------------

// IO functions

// Reads next token and return it as []byte
func readb() []byte {
	b, err := nextToken()
	if err != nil {
		panic(err)
	}
	return b
}

// Reads next token and return it as string
func reads() string {
	return string(readb())
}

// Read next line as []byte
func readbln() []byte {
	b, err := nextLine()
	if err != nil {
		panic(err)
	}
	return b
}

// Read next line as string
func readsln() string {
	return string(readbln())
}

// Reads next token and return it as int64
func readll() int64 {
	i, err := strconv.ParseInt(reads(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// Reads next token and return it as int
func readi() int {
	return int(readll())
}

// Reads next token and return it as float64
func readf() float64 {
	f, err := strconv.ParseFloat(reads(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// Write args to OutputWriter with the format f
func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(OutputWriter, f, args...)
}

// Write args to OutputWriter without format
func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(OutputWriter, args...)
}

// Write args to stderr with the format f
func eprintf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(os.Stderr, f, args...)
}

// Write args to stderr without format
func eprintln(args ...interface{}) (int, error) {
	return fmt.Fprintln(os.Stderr, args...)
}

// -----------------------------------------------------------------------------

// Simple math functions

const (
	// big prime
	INF  = 1000000007
	INF2 = 1000000009
	INF3 = 998244353
)

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

func minll(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

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

func maxll(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

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

func absll(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

// egcd(a, b) returns d, x, y:
//   d is gcd(a,b)
//   x, y are  integers that satisfy ax + by = d
func egcd(a, b int) (int, int, int) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcd(b, a%b)
	return d, y, x - a/b*y
}

func egcdll(a, b int64) (int64, int64, int64) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcdll(b, a%b)
	return d, y, x - a/b*y
}

func gcd(a, b int) int {
	d, _, _ := egcd(a, b)
	return d
}

func gcdll(a, b int64) int64 {
	d, _, _ := egcdll(a, b)
	return d
}

// set up IO functions
func init() {
	// for non-interactive
	SetInput(os.Stdin)
	SetOutput(os.Stdout)

	// Enable below when interactive.  Its ok to leave above intact.
	// SetInteractive(os.Stdout, os.Stdin)
}

type St struct {
	A, B int
}

func main() {
	defer Flush()

	N := readi()
	M := readi()
	W := make([]St, N)
	for i := range W {
		W[i].A = readi()
		W[i].B = readi()
	}
	pq := new(PriorityQueue)
	push := func(x St) {
		heap.Push(pq, x)
	}
	pop := func() St {
		x := heap.Pop(pq)
		return x.(St)
	}
	empty := func() bool {
		return pq.Len() == 0
	}
	Sort(W, func(i, j int) bool { return W[i].A < W[j].A })

	// 0 1 2 3 4 ... W
	//
	var ans, j int
	for d := 0; d <= M; d++ {
		for j < N && W[j].A <= d {
			push(W[j])
			j++
		}
		if !empty() {
			x := pop()
			ans += x.B
		}
	}
	println(ans)
}

type PriorityQueue []St

func (pq PriorityQueue) Len() int {
	return len(pq)
}

func (pq PriorityQueue) Less(i, j int) bool {
	return pq[i].B > pq[j].B
}

func (pq PriorityQueue) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
}

func (pq *PriorityQueue) Push(x interface{}) {
	old := *pq
	*pq = append(old, x.(St))
}

func (pq *PriorityQueue) Pop() interface{} {
	old := *pq
	n := len(old) - 1
	x := old[n]
	*pq = old[:n]
	return x
}

// =============================================================================

// Copyright 2017 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// name of functions are changed

// The function panics if the provided interface is not a slice.
func Sort(slice interface{}, less func(i, j int) bool) {
	rv := reflect.ValueOf(slice)
	swap := _sort_Swapper(slice)
	length := rv.Len()
	_sort_quickSort_func(_sort_lessSwap{less, swap}, 0, length, _sort_maxDepth(length))
}

func _sort_maxDepth(n int) int {
	var depth int
	for i := n; i > 0; i >>= 1 {
		depth++
	}
	return depth * 2
}

type _sort_lessSwap struct {
	Less func(i, j int) bool
	Swap func(i, j int)
}

// Auto-generated variant of sort.go:insertionSort
func _sort_insertionSort_func(data _sort_lessSwap, a, b int) {
	for i := a + 1; i < b; i++ {
		for j := i; j > a && data.Less(j, j-1); j-- {
			data.Swap(j, j-1)
		}
	}
}

// Auto-generated variant of sort.go:siftDown
func _sort_siftDown_func(data _sort_lessSwap, lo, hi, first int) {
	root := lo
	for {
		child := 2*root + 1
		if child >= hi {
			break
		}
		if child+1 < hi && data.Less(first+child, first+child+1) {
			child++
		}
		if !data.Less(first+root, first+child) {
			return
		}
		data.Swap(first+root, first+child)
		root = child
	}
}

// Auto-generated variant of sort.go:heapSort
func _sort_heapSort_func(data _sort_lessSwap, a, b int) {
	first := a
	lo := 0
	hi := b - a
	for i := (hi - 1) / 2; i >= 0; i-- {
		_sort_siftDown_func(data, i, hi, first)
	}
	for i := hi - 1; i >= 0; i-- {
		data.Swap(first, first+i)
		_sort_siftDown_func(data, lo, i, first)
	}
}

// Auto-generated variant of sort.go:medianOfThree
func _sort_medianOfThree_func(data _sort_lessSwap, m1, m0, m2 int) {
	if data.Less(m1, m0) {
		data.Swap(m1, m0)
	}
	if data.Less(m2, m1) {
		data.Swap(m2, m1)
		if data.Less(m1, m0) {
			data.Swap(m1, m0)
		}
	}
}

// Auto-generated variant of sort.go:doPivot
func _sort_doPivot_func(data _sort_lessSwap, lo, hi int) (midlo, midhi int) {
	m := int(uint(lo+hi) >> 1)
	if hi-lo > 40 {
		s := (hi - lo) / 8
		_sort_medianOfThree_func(data, lo, lo+s, lo+2*s)
		_sort_medianOfThree_func(data, m, m-s, m+s)
		_sort_medianOfThree_func(data, hi-1, hi-1-s, hi-1-2*s)
	}
	_sort_medianOfThree_func(data, lo, m, hi-1)
	pivot := lo
	a, c := lo+1, hi-1
	for ; a < c && data.Less(a, pivot); a++ {
	}
	b := a
	for {
		for ; b < c && !data.Less(pivot, b); b++ {
		}
		for ; b < c && data.Less(pivot, c-1); c-- {
		}
		if b >= c {
			break
		}
		data.Swap(b, c-1)
		b++
		c--
	}
	protect := hi-c < 5
	if !protect && hi-c < (hi-lo)/4 {
		dups := 0
		if !data.Less(pivot, hi-1) {
			data.Swap(c, hi-1)
			c++
			dups++
		}
		if !data.Less(b-1, pivot) {
			b--
			dups++
		}
		if !data.Less(m, pivot) {
			data.Swap(m, b-1)
			b--
			dups++
		}
		protect = dups > 1
	}
	if protect {
		for {
			for ; a < b && !data.Less(b-1, pivot); b-- {
			}
			for ; a < b && data.Less(a, pivot); a++ {
			}
			if a >= b {
				break
			}
			data.Swap(a, b-1)
			a++
			b--
		}
	}
	data.Swap(pivot, b-1)
	return b - 1, c
}

// Auto-generated variant of sort.go:quickSort
func _sort_quickSort_func(data _sort_lessSwap, a, b, maxDepth int) {
	for b-a > 12 {
		if maxDepth == 0 {
			_sort_heapSort_func(data, a, b)
			return
		}
		maxDepth--
		mlo, mhi := _sort_doPivot_func(data, a, b)
		if mlo-a < b-mhi {
			_sort_quickSort_func(data, a, mlo, maxDepth)
			a = mhi
		} else {
			_sort_quickSort_func(data, mhi, b, maxDepth)
			b = mlo
		}
	}
	if b-a > 1 {
		for i := a + 6; i < b; i++ {
			if data.Less(i, i-6) {
				data.Swap(i, i-6)
			}
		}
		_sort_insertionSort_func(data, a, b)
	}
}

// ----------------------------------------------------------------------------

func _sort_Swapper(slice interface{}) func(i, j int) {
	v := reflect.ValueOf(slice)
	vdata := v.Pointer()
	vlen := v.Len()
	vcap := v.Cap()

	sz := int(v.Type().Elem().Size())

	// for typical small elements
	switch sz {
	case 24: // for slice
		var s [][3]int64
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen
		h.Cap = vcap
		return func(i, j int) { s[i], s[j] = s[j], s[i] }
	case 16: // for string
		var s [][2]int64
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen
		h.Cap = vcap
		return func(i, j int) { s[i], s[j] = s[j], s[i] }
	case 8:
		var s []int64
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen
		h.Cap = vcap
		return func(i, j int) { s[i], s[j] = s[j], s[i] }
	case 4:
		var s []int32
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen
		h.Cap = vcap
		return func(i, j int) { s[i], s[j] = s[j], s[i] }
	case 2:
		var s []int16
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen
		h.Cap = vcap
		return func(i, j int) { s[i], s[j] = s[j], s[i] }
	case 1:
		var s []int8
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen
		h.Cap = vcap
		return func(i, j int) { s[i], s[j] = s[j], s[i] }
	}

	// for large elements
	if sz%16 == 0 {
		m := sz / 16
		var s [][2]int64
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen * m
		h.Cap = vcap * m
		return func(i, j int) {
			for k := 0; k < m; k++ {
				ri := i*m + k
				rj := j*m + k
				s[ri], s[rj] = s[rj], s[ri]
			}
		}
	}
	if sz%8 == 0 {
		m := sz / 8
		var s []int64
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen * m
		h.Cap = vcap * m
		return func(i, j int) {
			for k := 0; k < m; k++ {
				ri := i*m + k
				rj := j*m + k
				s[ri], s[rj] = s[rj], s[ri]
			}
		}
	}
	if sz%4 == 0 {
		m := sz / 4
		var s []int32
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen * m
		h.Cap = vcap * m
		return func(i, j int) {
			for k := 0; k < m; k++ {
				ri := i*m + k
				rj := j*m + k
				s[ri], s[rj] = s[rj], s[ri]
			}
		}
	}
	if sz%2 == 0 {
		m := sz / 2
		var s []int16
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen * m
		h.Cap = vcap * m
		return func(i, j int) {
			for k := 0; k < m; k++ {
				ri := i*m + k
				rj := j*m + k
				s[ri], s[rj] = s[rj], s[ri]
			}
		}
	} else {
		m := sz
		var s []int8
		h := (*reflect.SliceHeader)(unsafe.Pointer(&s))
		h.Data = vdata
		h.Len = vlen * m
		h.Cap = vcap * m
		return func(i, j int) {
			for k := 0; k < m; k++ {
				ri := i*m + k
				rj := j*m + k
				s[ri], s[rj] = s[rj], s[ri]
			}
		}
	}
}

// =============================================================================