Problem:


Score : 1000 points

Problem Statement

There are M chairs arranged in a line. The coordinate of the i-th chair (1 ≤ i ≤ M) is i.

N people of the Takahashi clan played too much games, and they are all suffering from backaches. They need to sit in chairs and rest, but they are particular about which chairs they sit in. Specifically, the i-th person wishes to sit in a chair whose coordinate is not greater than L_i, or not less than R_i. Naturally, only one person can sit in the same chair.

It may not be possible for all of them to sit in their favorite chairs, if nothing is done.
Aoki, who cares for the health of the people of the Takahashi clan, decides to provide additional chairs so that all of them can sit in chairs at their favorite positions.

Additional chairs can be placed at arbitrary real coordinates. Find the minimum required number of additional chairs.

Constraints

1 ≤ N,M ≤ 2 × 10^5

0 ≤ L_i < R_i ≤ M + 1(1 ≤ i ≤ N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1
:
L_N R_N

Output

Print the minimum required number of additional chairs.

Sample Input 1

4 4
0 3
2 3
1 3
3 4

Sample Output 1

0

The four people can sit in chairs at the coordinates 3, 2, 1 and 4, respectively, and no more chair is needed.

Sample Input 2

7 6
0 7
1 5
3 6
2 7
1 6
2 6
3 7

Sample Output 2

2

If we place additional chairs at the coordinates 0 and 2.5, the seven people can sit at coordinates 0, 5, 3, 2, 6, 1 and 2.5, respectively.

Sample Input 3

3 1
1 2
1 2
1 2

Sample Output 3

2

Sample Input 4

6 6
1 6
1 6
1 5
1 5
2 6
2 6

Sample Output 4

2



Sample input:
4 4
0 3
2 3
1 3
3 4


Sample output:
0

Submission status: Time Limit Exceeded

Solution code:
from collections import deque

class LazySegtree():
    def __init__(self,n,init_val,merge_func,ide_ele):
        self.n=n
        self.ide_ele=ide_ele
        self.merge_func=merge_func
        self.val=[0 for i in range(1<<n)]
        self.merge=[0 for i in range(1<<n)]
        self.parent=[-1 for i in range(1<<n)]
        self.lazy=[0 for i in range(1<<n)]
        deq=deque([1<<(n-1)])
        res=[]
        while deq:
            v=deq.popleft()
            res.append(v)
            if not v&1:
                gap=(v&-v)//2
                self.parent[v-gap]=v
                deq.append(v-gap)
                self.parent[v+gap]=v
                deq.append(v+gap)
        for v in res[::-1]:
            if v-1<len(init_val):
                self.val[v-1]=init_val[v-1]
            else:
                self.val[v-1]=10**18
            self.merge[v-1]=self.val[v-1]
            if not v&1:
                gap=(v&-v)//2
                self.merge[v-1]=self.merge_func(self.merge[v-1],self.merge[v-gap-1],self.merge[v+gap-1])

    def lower_kth_update(self,nd,k,x):
        if k==-1:
            return
        maxi=nd-(nd&-nd)+1+k
        pos=nd
        while True:
            gap=(pos&-pos)//2
            if self.lazy[pos-1]:
                self.val[pos-1]+=self.lazy[pos-1]
                self.merge[pos-1]+=self.lazy[pos-1]
                if not pos&1:
                    self.lazy[pos-gap-1]+=self.lazy[pos-1]
                    self.lazy[pos+gap-1]+=self.lazy[pos-1]
                self.lazy[pos-1]=0
            if pos>maxi:
                pos-=gap
            elif pos==maxi:
                self.val[pos-1]+=x
                if not pos&1:
                    self.lazy[pos-gap-1]+=x
                break
            else:
                self.val[pos-1]+=x
                self.lazy[pos-gap-1]+=x
                pos+=gap

        while pos!=self.parent[nd]:
            if pos&1:
                self.merge[pos-1]=self.val[pos-1]
            else:
                gap=(pos&-pos)//2
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            pos=self.parent[pos]

    def upper_kth_update(self,nd,k,x):
        if k==-1:
            return
        mini=nd+(nd&-nd)-1-k
        pos=nd
        while True:
            gap=(pos&-pos)//2
            if self.lazy[pos-1]:
                self.val[pos-1]+=self.lazy[pos-1]
                self.merge[pos-1]+=self.lazy[pos-1]
                if not pos&1:
                    self.lazy[pos-gap-1]+=self.lazy[pos-1]
                    self.lazy[pos+gap-1]+=self.lazy[pos-1]
                self.lazy[pos-1]=0
            if pos>mini:
                self.val[pos-1]+=x
                self.lazy[pos+gap-1]+=x
                pos-=gap
            elif pos==mini:
                self.val[pos-1]+=x
                if not pos&1:
                    self.lazy[pos+gap-1]+=x
                break
            else:
                pos+=gap

        while pos!=self.parent[nd]:
            if pos&1:
                self.merge[pos-1]=self.val[pos-1]
            else:
                gap=(pos&-pos)//2
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            pos=self.parent[pos]

    def update(self,l,r,x):
        pos=1<<(self.n-1)
        while True:
            if self.lazy[pos-1]:
                self.val[pos-1]+=self.lazy[pos-1]
                self.merge[pos-1]+=self.lazy[pos-1]
                if not pos&1:
                    self.lazy[pos-gap-1]+=self.lazy[pos-1]
                    self.lazy[pos+gap-1]+=self.lazy[pos-1]
                self.lazy[pos-1]=0
            if pos-1<l:
                pos+=(pos&-pos)//2
            elif pos-1>r:
                pos-=(pos&-pos)//2
            else:
                self.val[pos-1]+=x
                gap=(pos&-pos)//2
                self.upper_kth_update(pos-gap,pos-1-l-1,x)
                self.lower_kth_update(pos+gap,r-pos,x)
                break

        while self.parent[pos]!=-1:
            if pos&1:
                self.merge[pos-1]=self.val[pos-1]
            else:
                gap=(pos&-pos)//2
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            pos=self.parent[pos]

    def lower_kth_merge(self,nd,k,debug=False):
        res=self.ide_ele
        if k==-1:
            return res
        maxi=nd-(nd&-nd)+1+k
        pos=nd
        while True:
            gap=(pos&-pos)//2
            if self.lazy[pos-1]:
                self.val[pos-1]+=self.lazy[pos-1]
                self.merge[pos-1]+=self.lazy[pos-1]
                if not pos&1:
                    self.lazy[pos-gap-1]+=self.lazy[pos-1]
                    self.lazy[pos+gap-1]+=self.lazy[pos-1]
                self.lazy[pos-1]=0
            if pos>maxi:
                pos-=gap
            elif pos==maxi:
                break
            else:
                pos+=gap

        while pos!=self.parent[nd]:
            gap=(pos&-pos)//2
            if pos&1:
                self.merge[pos-1]=self.val[pos-1]
            else:
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            if pos<=maxi:
                res=self.merge_func(res,self.val[pos-1])
                if not pos&1:
                    res=self.merge_func(res,self.merge[pos-gap-1]+self.lazy[pos-gap-1])
            pos=self.parent[pos]
        return res

    def upper_kth_merge(self,nd,k):
        res=self.ide_ele
        if k==-1:
            return res
        mini=nd+(nd&-nd)-1-k
        pos=nd
        while True:
            gap=(pos&-pos)//2
            if self.lazy[pos-1]:
                self.val[pos-1]+=self.lazy[pos-1]
                self.merge[pos-1]+=self.lazy[pos-1]
                if not pos&1:
                    self.lazy[pos-gap-1]+=self.lazy[pos-1]
                    self.lazy[pos+gap-1]+=self.lazy[pos-1]
                self.lazy[pos-1]=0
            if pos>mini:
                pos-=gap
            elif pos==mini:
                break
            else:
                pos+=gap

        while pos!=self.parent[nd]:
            gap=(pos&-pos)//2
            if pos&1:
                self.merge[pos-1]=self.val[pos-1]
            else:
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            if pos>=mini:
                res=self.merge_func(res,self.val[pos-1])
                if not pos&1:
                    res=self.merge_func(res,self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            pos=self.parent[pos]
        return res

    def query(self,l,r):
        pos=1<<(self.n-1)
        res=self.ide_ele
        while True:
            gap=(pos&-pos)//2
            if self.lazy[pos-1]:
                self.val[pos-1]+=self.lazy[pos-1]
                self.merge[pos-1]+=self.lazy[pos-1]
                if not pos&1:
                    self.lazy[pos-gap-1]+=self.lazy[pos-1]
                    self.lazy[pos+gap-1]+=self.lazy[pos-1]
                self.lazy[pos-1]=0
            if pos-1<l:
                pos+=(pos&-pos)//2
            elif pos-1>r:
                pos-=(pos&-pos)//2
            else:
                left=self.upper_kth_merge(pos-gap,pos-1-l-1)
                right=self.lower_kth_merge(pos+gap,r-pos)
                res=self.merge_func(left,right,self.val[pos-1])
                return res

import sys

input=sys.stdin.buffer.readline

ide_ele=10**18

def segfunc(*args):
    return min(args)

N,M=map(int,input().split())

init=[0 for i in range(M+2)]
for i in range(1,M+1):
    init[0]+=1
    init[i+1]-=1
for i in range(1,M+1):
    init[i]+=init[i-1]
init[-1]=0

LST=LazySegtree((M+2).bit_length(),init,segfunc,ide_ele)

hito=[tuple(map(int,input().split())) for i in range(N)]
hito.sort()

add=M-N
for l,r in hito:
    LST.update(0,r,-1)
    m=LST.query(l+1,M+1)+l
    add=min(m,add)

print(max(-add,0))

Submission status: Time Limit Exceeded

Solution code:
import sys

input=sys.stdin.readline

N,M=map(int,input().split())

m=int((M+2)**.5)
isu=[0]*(M+2)
isudata=[0]*((M+1)//m+1)
RMQdata=[0]*((M+1)//m+1)

def update(l,r,x):
    id=l
    while id<=r:
        L=id
        q=id//m
        R=min(m*(q+1)-1,r)
        if R-L+1==m:
            isudata[q]+=x
            RMQdata[q]+=x
        else:
            for i in range(L,R+1):
                isu[i]+=x
            res=2**31
            for i in range(m*q,min(M+2,m*(q+1))):
                test=isu[i]+isudata[q]
                res=min(res,test)
            RMQdata[q]=res
        id=R+1

def query(l,r):
    id=l
    res=2**31
    while id<=r:
        L=id
        q=id//m
        R=min(m*(q+1)-1,r)
        if R-L+1==m:
            res=min(res,RMQdata[q])
        else:
            for i in range(L,R+1):
                test=isu[i]+isudata[q]
                res=min(res,test)
        id=R+1

    return res

for i in range(1,M+1):
    update(0,i,1)

add=M-N
hito=[]
for i in range(N):
    L,R=map(int,input().split())
    hito.append((L,R))
hito.sort()

for l,r in hito:
    update(0,r,-1)
    t=query(l+1,M+1)+l
    add=min(t,add)

print(max(-add,0))

Submission status: Time Limit Exceeded

Solution code:
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

# 区間加算、区間最大
class LazySeg:
    def __init__(self, aa):
        inf = 10 ** 16
        n = 1 << (len(aa) - 1).bit_length()
        tree = [-inf] * (2 * n - 1)
        lazy = [0] * (2 * n - 1)
        tree[n - 1:n - 1 + len(aa)] = aa
        for u in range(n - 2, -1, -1):
            tree[u] = max(tree[u * 2 + 1], tree[u * 2 + 2])
        self.tree = tree
        self.lazy = lazy
        self.n = n
        self.inf = inf

    def prop(self, u, l, r):
        self.tree[u] += self.lazy[u]
        if l + 1 < r:
            self.lazy[u * 2 + 1] += self.lazy[u]
            self.lazy[u * 2 + 2] += self.lazy[u]
        self.lazy[u] = 0

    def add(self, l, r, a, u=0, tl=0, tr=-1):
        if tr == -1: tr = self.n
        if r <= tl or tr <= l: return
        if l <= tl and tr <= r:
            self.lazy[u] += a
            self.prop(u, tl, tr)
            return
        tm = (tl + tr) // 2
        self.prop(u, tl, tr)
        self.add(l, r, a, u * 2 + 1, tl, tm)
        self.add(l, r, a, u * 2 + 2, tm, tr)
        self.tree[u] = max(self.tree[u * 2 + 1], self.tree[u * 2 + 2])

    def max(self, l, r, u=0, tl=0, tr=-1):
        res = -self.inf
        if tr == -1: tr = self.n
        if r <= tl or tr <= l: return res
        self.prop(u, tl, tr)
        if l <= tl and tr <= r:
            return self.tree[u]
        tm = (tl + tr) // 2
        ret = self.max(l, r, u * 2 + 1, tl, tm)
        if ret > res: res = ret
        ret = self.max(l, r, u * 2 + 2, tm, tr)
        if ret > res: res = ret
        return res

def main():
    n,m=MI()
    lr=[LI() for _ in range(n)]
    lr.sort()
    #print(lr)
    aa=list(range(-m,1))
    st=LazySeg(aa)
    ans=max(n-m,0)
    for i,[l,r] in enumerate(lr):
        st.add(0,r,1)
        if i+1<n and lr[i+1][0]==l:continue
        #print(st.max(0,m+1),l)
        over=st.max(0,m+1)-l
        if over>ans:ans=over
    print(ans)

main()

Submission status: Time Limit Exceeded

Solution code:
# coding: utf-8
import array, bisect, collections, copy, heapq, itertools, math, random, re, string, sys, time
sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


def II(): return int(input())
def ILI(): return list(map(int, input().split()))
def IAI(LINE): return [ILI() for __ in range(LINE)]
def IDI(): return {key: value for key, value in ILI()}


def read():
    N, M = ILI()
    people = [ILI() for __ in range(N)]
    return N, M, people


def solve(N, M, people):
    bool_chair = [False] * (M + 2)
    bool_chair[0], bool_chair[M + 1] = True, True
    people.sort(key=lambda x: (-x[0], x[1]))
    ans = 0
    for person in people:
        update = False
        for i in range(person[0], 0, -1):
            if bool_chair[i] is False:
                bool_chair[i] = True
                update = True
                break
        if update is False:
            for i in range(person[1], M + 1):
                if bool_chair[i] is False:
                    bool_chair[i] = True
                    update = True
                    break
            if update is False:
                ans += 1
    return ans


def main():
    params = read()
    print(solve(*params))


if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
from operator import add

class LazySegmentTree():
    def __init__(self,n,init,merge=min,merge_unit=10**18,operate=add,operate_unit=0):
        self.merge=merge
        self.merge_unit=merge_unit
        self.operate=operate
        self.operate_unit=operate_unit

        self.n=(n-1).bit_length()
        self.data=[0 for i in range(1<<(self.n+1))]
        self.lazy=[0 for i in range(1<<(self.n+1))]
        for i in range(n):
            self.data[2**self.n+i]=init[i]
        for i in range(2**self.n-1,0,-1):
            self.data[i]=self.merge(self.data[2*i],self.data[2*i+1])

    def propagate_above(self,i):
        m=i.bit_length()-1
        for bit in range(m,0,-1):
            v=i>>bit
            add=self.lazy[v]
            self.lazy[v]=0
            self.data[2*v]=self.operate(self.data[2*v],add)
            self.data[2*v+1]=self.operate(self.data[2*v+1],add)
            self.lazy[2*v]=self.operate(self.lazy[2*v],add)
            self.lazy[2*v+1]=self.operate(self.lazy[2*v+1],add)


    def remerge_above(self,i):
        while i:
            i>>=1
            self.data[i]=self.operate(self.merge(self.data[2*i],self.data[2*i+1]),self.lazy[i])

    def update(self,l,r,x):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        while l<r:
            if l&1:
                self.data[l]=self.operate(self.data[l],x)
                self.lazy[l]=self.operate(self.lazy[l],x)
                l+=1
            if r&1:
                self.data[r-1]=self.operate(self.data[r-1],x)
                self.lazy[r-1]=self.operate(self.lazy[r-1],x)
            l>>=1
            r>>=1
        self.remerge_above(l0)
        self.remerge_above(r0)

    def query(self,l,r):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        res=self.merge_unit
        while l<r:
            if l&1:
                res=self.merge(res,self.data[l])
                l+=1
            if r&1:
                res=self.merge(res,self.data[r-1])
            l>>=1
            r>>=1
        return res

import sys

input=sys.stdin.buffer.readline

ide_ele=10**18

N,M=map(int,input().split())

init=[0 for i in range(M+2)]
for i in range(1,M+1):
    init[0]+=1
    init[i+1]-=1
for i in range(1,M+1):
    init[i]+=init[i-1]
init[-1]=0

LST=LazySegmentTree(M+2,init)

hito=[tuple(map(int,input().split())) for i in range(N)]
hito.sort()

add=M-N
for l,r in hito:
    LST.update(0,r+1,-1)
    m=LST.query(l+1,M+2)+l
    add=min(m,add)

print(max(-add,0))

Submission status: Accepted

Solution code:
class LazySegmentTree():
    def __init__(self,n,init,merge_func=min,ide_ele=10**18):
        self.n=(n-1).bit_length()
        self.merge_func=merge_func
        self.ide_ele=ide_ele
        self.data=[0 for i in range(1<<(self.n+1))]
        self.lazy=[0 for i in range(1<<(self.n+1))]
        for i in range(n):
            self.data[2**self.n+i]=init[i]
        for i in range(2**self.n-1,0,-1):
            self.data[i]=self.merge_func(self.data[2*i],self.data[2*i+1])

    def propagate_above(self,i):
        m=i.bit_length()-1
        for bit in range(m,0,-1):
            v=i>>bit
            add=self.lazy[v]
            self.lazy[v]=0
            self.data[2*v]+=add
            self.data[2*v+1]+=add
            self.lazy[2*v]+=add
            self.lazy[2*v+1]+=add

    def remerge_above(self,i):
        while i:
            i>>=1
            self.data[i]=self.merge_func(self.data[2*i],self.data[2*i+1])+self.lazy[i]

    def update(self,l,r,x):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        while l<r:
            self.data[l]+=x*(l&1)
            self.lazy[l]+=x*(l&1)
            l+=(l&1)
            self.data[r-1]+=x*(r&1)
            self.lazy[r-1]+=x*(r&1)
            l>>=1
            r>>=1
        self.remerge_above(l0)
        self.remerge_above(r0)

    def query(self,l,r):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        res=self.ide_ele
        while l<r:
            if l&1:
                res=self.merge_func(res,self.data[l])
                l+=1
            if r&1:
                res=self.merge_func(res,self.data[r-1])
            l>>=1
            r>>=1
        return res

import sys

input=sys.stdin.buffer.readline

ide_ele=10**18

N,M=map(int,input().split())

init=[0 for i in range(M+2)]
for i in range(1,M+1):
    init[0]+=1
    init[i+1]-=1
for i in range(1,M+1):
    init[i]+=init[i-1]
init[-1]=0

LST=LazySegmentTree(M+2,init)

hito=[tuple(map(int,input().split())) for i in range(N)]
hito.sort()

add=M-N
for l,r in hito:
    LST.update(0,r+1,-1)
    m=LST.query(l+1,M+2)+l
    add=min(m,add)

print(max(-add,0))

Submission status: Accepted

Solution code:
from collections import deque

class LazySegtree():
    def __init__(self,n,init_val,merge_func,ide_ele):
        self.n=n
        self.ide_ele=ide_ele
        self.merge_func=merge_func
        self.val=[0 for i in range(1<<n)]
        self.merge=[0 for i in range(1<<n)]
        self.parent=[-1 for i in range(1<<n)]
        self.lazy=[0 for i in range(1<<n)]
        deq=deque([1<<(n-1)])
        res=[]
        while deq:
            v=deq.popleft()
            res.append(v)
            if not v&1:
                gap=(v&-v)//2
                self.parent[v-gap]=v
                deq.append(v-gap)
                self.parent[v+gap]=v
                deq.append(v+gap)
        for v in res[::-1]:
            if v-1<len(init_val):
                self.val[v-1]=init_val[v-1]
            else:
                self.val[v-1]=10**18
            self.merge[v-1]=self.val[v-1]
            if not v&1:
                gap=(v&-v)//2
                self.merge[v-1]=self.merge_func(self.merge[v-1],self.merge[v-gap-1],self.merge[v+gap-1])

    def lower_kth_update(self,nd,k,x):
        if k==-1:
            return
        maxi=nd-(nd&-nd)+1+k
        ids=self.idgetter(nd,maxi)
        for pos in ids:
            gap=(pos&-pos)//2
            self.propagate(pos)
            if pos<=maxi:
                self.val[pos-1]+=x
                self.lazy[pos-gap-1]+=x*(gap!=0)

        if pos&1:
            self.merge[pos-1]=self.val[pos-1]
            ids.pop()
        ids=ids[::-1]
        for pos in ids:
            gap=(pos&-pos)//2
            self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])

    def upper_kth_update(self,nd,k,x):
        if k==-1:
            return
        mini=nd+(nd&-nd)-1-k
        ids=self.idgetter(nd,mini)
        for pos in ids:
            gap=(pos&-pos)//2
            self.propagate(pos)
            if pos>=mini:
                self.val[pos-1]+=x
                self.lazy[pos+gap-1]+=x*(gap!=0)

        if pos&1:
            self.merge[pos-1]=self.val[pos-1]
            ids.pop()
        ids=ids[::-1]
        for pos in ids:
            gap=(pos&-pos)//2
            self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])

    def update(self,l,r,x):
        pos=1<<(self.n-1)
        end=self.range_goal(l+1,r+1)
        ids=self.idgetter(pos,end)
        for pos in ids:
            self.propagate(pos)
        gap=(pos&-pos)//2
        self.val[pos-1]+=x
        self.upper_kth_update(pos-gap,pos-1-l-1,x)
        self.lower_kth_update(pos+gap,r-pos,x)

        if pos&1:
            self.merge[pos-1]=self.val[pos-1]
            ids.pop()
        for pos in ids[::-1]:
            gap=(pos&-pos)//2
            self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])

    def lower_kth_merge(self,nd,k,debug=False):
        res=self.ide_ele
        if k==-1:
            return res
        maxi=nd-(nd&-nd)+1+k
        ids=self.idgetter(nd,maxi)
        for pos in ids:
            self.propagate(pos)

        stack=[self.ide_ele]
        if pos&1:
            self.merge[pos-1]=self.val[pos-1]
            stack.append(self.merge[pos-1])
            ids.pop()
        for pos in ids[::-1]:
            gap=(pos&-pos)//2
            if pos<=maxi:
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1])
                stack.append(self.merge[pos-1])
                self.merge[pos-1]=self.merge_func(self.merge[pos-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
            else:
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
        return self.merge_func(stack)

    def upper_kth_merge(self,nd,k):
        res=self.ide_ele
        if k==-1:
            return res
        mini=nd+(nd&-nd)-1-k
        ids=self.idgetter(nd,mini)
        for pos in ids:
            self.propagate(pos)

        stack=[self.ide_ele]
        if pos&1:
            self.merge[pos-1]=self.val[pos-1]
            stack.append(self.merge[pos-1])
            ids.pop()
        for pos in ids[::-1]:
            gap=(pos&-pos)//2
            if pos>=mini:
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
                stack.append(self.merge[pos-1])
                self.merge[pos-1]=self.merge_func(self.merge[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1])
            else:
                self.merge[pos-1]=self.merge_func(self.val[pos-1],self.merge[pos-gap-1]+self.lazy[pos-gap-1],self.merge[pos+gap-1]+self.lazy[pos+gap-1])
        return self.merge_func(stack)

    def query(self,l,r):
        pos=1<<(self.n-1)
        end=self.range_goal(l+1,r+1)
        ids=self.idgetter(pos,end)
        for pos in ids:
            self.propagate(pos)
        gap=(pos&-pos)//2
        left=self.upper_kth_merge(pos-gap,pos-1-l-1)
        right=self.lower_kth_merge(pos+gap,r-pos)
        res=self.merge_func(left,right,self.val[pos-1])
        return res

    def propagate(self,pos):
        if self.lazy[pos-1]:
            self.val[pos-1]+=self.lazy[pos-1]
            self.merge[pos-1]+=self.lazy[pos-1]
            if not pos&1:
                gap=(pos&-pos)//2
                self.lazy[pos-gap-1]+=self.lazy[pos-1]
                self.lazy[pos+gap-1]+=self.lazy[pos-1]
            self.lazy[pos-1]=0
        return

    def idgetter(self,start,goal):
        res=[]
        pos=goal
        while pos!=start:
            res.append(pos)
            pos=self.parent[pos]
        res.append(start)
        return res[::-1]

    def range_goal(self,l,r):
        n=(l^r).bit_length()-1
        m=(l&-l).bit_length()-1
        if n>m:
            return (r>>n)<<n
        else:
            return l

import sys

input=sys.stdin.buffer.readline

ide_ele=10**18

N,M=map(int,input().split())

init=[0 for i in range(M+2)]
for i in range(1,M+1):
    init[0]+=1
    init[i+1]-=1
for i in range(1,M+1):
    init[i]+=init[i-1]
init[-1]=0

LST=LazySegtree((M+2).bit_length(),init,merge_func=min,ide_ele=10**18)

hito=[tuple(map(int,input().split())) for i in range(N)]
hito.sort()

add=M-N
for l,r in hito:
    LST.update(0,r,-1)
    m=LST.query(l+1,M+1)+l
    add=min(m,add)

print(max(-add,0))