#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=100007;
int read(){
    int ans=0,f=1,c=getchar();
    while(c<‘0‘||c>‘9‘){if(c==‘-‘) f=-1; c=getchar();}
    while(c>=‘0‘&&c<=‘9‘){ans=ans*10+(c-‘0‘); c=getchar();}
    return ans*f;
}
int n,m,cnt,nl,nr,ans,sum;
struct node{
    int l,r;
    bool operator<(const node &x)const{return l<x.l;}
}e[M],q[M];
int cal(int x){return x?q[x].l-q[x-1].r:0;}
int main()
{
    while(scanf("%d %d",&n,&m)==2){
        for(int i=0;i<n;i++) e[i].l=read(),e[i].r=read()+1;
        sort(e,e+n);
        cnt=0; int ll=e[0].l,rr=e[0].r;
        for(int i=1;i<n;i++){
            if(e[i].r<=rr) continue;
            if(e[i].l<=rr) rr=e[i].r;
            else q[++cnt]=(node){ll,rr},ll=e[i].l,rr=e[i].r;
        }
        q[++cnt]=(node){ll,rr};
        ans=0;
        for(int i=0,j=0,cost=0;i<=cnt;i++){
            int s=q[i].r-q[j].l;
            cost+=cal(i);
            while(cost>m){
                j++;
                s=q[i].r-q[j].l;
                cost-=cal(j);
            }
            ans=max(ans,s-cost+m);
        }printf("%d\n",ans);
    }
    return 0;
}