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

Solution (Python):
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*(bool(gap))
        for pos in ids[::-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])

    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*(bool(gap))
        for pos in ids[::-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])

    def update(self,l,r,x):
        pos=1<<(self.n-1)
        while True:
            gap=(pos&-pos)//2
            self.propagate(pos)
            if pos-1<l:
                pos+=(pos&-pos)//2
            elif pos-1>r:
                pos-=(pos&-pos)//2
            else:
                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)
                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
        ids=self.idgetter(nd,maxi)
        for pos in ids:
            self.propagate(pos)

        stack=[self.ide_ele]
        for pos in ids[::-1]:
            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:
                stack.append(self.val[pos-1])
                if not pos&1:
                    stack.append(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]
        for pos in ids[::-1]:
            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:
                stack.append(self.val[pos-1])
                if not pos&1:
                    stack.append(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)
        res=self.ide_ele
        while True:
            gap=(pos&-pos)//2
            self.propagate(pos)
            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

    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]

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))

Solution (Python):
import sys

input=sys.stdin.readline

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


INF = 2**31-1

LV = (M+2-1).bit_length()
N0 = 2**LV
data = [0]*(2*N0)
lazy = [0]*(2*N0)

def gindex(l, r):
    L = (l + N0) >> 1; R = (r + N0) >> 1
    lc = 0 if l & 1 else (L & -L).bit_length()
    rc = 0 if r & 1 else (R & -R).bit_length()
    for i in range(LV):
        if rc <= i:
            yield R
        if L < R and lc <= i:
            yield L
        L >>= 1; R >>= 1


def propagates(*ids):
    for i in reversed(ids):
        v = lazy[i-1]
        if not v:
            continue
        lazy[2*i-1] += v; lazy[2*i] += v
        data[2*i-1] += v; data[2*i] += v
        lazy[i-1] = 0


def update(l, r, x):
    *ids, = gindex(l, r)
    propagates(*ids)

    L = N0 + l; R = N0 + r
    while L < R:
        if R & 1:
            R -= 1
            lazy[R-1] += x; data[R-1] += x
        if L & 1:
            lazy[L-1] += x; data[L-1] += x
            L += 1
        L >>= 1; R >>= 1
    for i in ids:
        data[i-1] = min(data[2*i-1], data[2*i])


def query(l, r):
    propagates(*gindex(l, r))
    L = N0 + l; R = N0 + r

    s = INF
    while L < R:
        if R & 1:
            R -= 1
            s = min(s, data[R-1])
        if L & 1:
            s = min(s, data[L-1])
            L += 1
        L >>= 1; R >>= 1
    return s

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

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,-1)
    
    
    m=query(l+1,M+2)+l
    add=min(m,add)

print(max(-add,0))

Solution (Python):
from operator import itemgetter
from heapq import heappush, heappop
N, M = map(int, input().split())
LR = [list(map(int, input().split())) for _ in range(N)]
LR.sort(key=itemgetter(1))
A = []
ans_left = 0
idx = 1
for _, r in LR:
    if r==M+1 or idx==M+1:
        break
    ans_left += 1
    idx = max(idx+1, r+1)

idx_LR = 0
q = []
for i in range(M+1-ans_left, M+1):
    while idx_LR<N and LR[idx_LR][1]<=i:
        l, _ = LR[idx_LR]
        heappush(q, l)
        idx_LR += 1
    heappop(q)
while idx_LR<N:
    l, _ = LR[idx_LR]
    q.append(l)
    idx_LR += 1

q.sort(reverse=True)
ans_right = 0
idx = M
for l in q:
    if l==0 or idx==0 or ans_right+ans_left==M:
        break
    ans_right += 1
    idx = min(l-1, idx-1)
ans = N - ans_left - ans_right
print(ans)