#include<bits/stdc++.h>
#define N 200005
using namespace std;
const long long inf=1e18;
int n,Q,b[N],L[N],R[N],bl[N],Len,p[N];
long long a[N],tag[N],sum[N],sum1[N],bj[N];
int read() {
	int kkk=0,x=1;
	char c=getchar();
	while((c<'0' || c>'9') && c!='-') c=getchar();
	if(c=='-') c=getchar(),x=-1;
	while(c>='0' && c<='9') kkk=kkk*10+(c-'0'),c=getchar();
	return kkk*x;
}
void Down(int x) {
	if(bj[x]!=inf) {
		for(int l0=L[x],r0=R[x]; l0<=r0; ++l0)a[l0]=bj[x]+tag[x];
	} else if(tag[x]) {
		for(int l0=L[x],r0=R[x]; l0<=r0; ++l0)a[l0]+=tag[x];
	}
	tag[x]=0,bj[x]=inf;
}
bool cmp(int x,int y) {
	return a[x]<a[y];
}
void Update(int x) {
	sort(p+L[x],p+R[x]+1,cmp),sum1[L[x]]=b[p[L[x]]];
	for(int l0=L[x]+1,r0=R[x]; l0<=r0; ++l0)sum1[l0]=sum1[l0-1]+b[p[l0]];
	tag[x]=0,bj[x]=inf;
}
int Find(int l,int r,long long x) {
	int mid,ans=0;
	while(l<=r) {
		mid=(l+r)>>1;
		if(a[p[mid]]<=x)ans=mid,l=mid+1;
		else r=mid-1;
	}
	return ans;
}
bool Check(int l,int r,long long x) {
	long long ans=0;
	if(bl[l]==bl[r]) {
		Down(bl[l]);
		for(int i=l; i<=r; ++i)if(a[i]<=x)ans+=b[i];
	} else {
		Down(bl[l]),Down(bl[r]);
		for(int j=L[bl[r]]; j<=r; ++j)if(a[j]<=x)ans+=b[j];
		for(int j=R[bl[l]]; j>=l; --j)if(a[j]<=x)ans+=b[j];
		for(int j=bl[l]+1; j<bl[r]; ++j)
			if(bj[j]!=1e18) {
				if(bj[j]+tag[j]<=x)ans+=sum[R[j]]-sum[L[j]-1];
			} else ans+=sum1[Find(L[j],R[j],x-tag[j])];
	}
	return ans*2>=sum[r]-sum[l-1];
}
int main() {
	n=read(),Q=read(),Len=619;
	for(int i=1; i<=n; ++i)a[i]=read(),p[i]=i,bj[i]=inf;
	for(int i=1; i<=n; ++i)b[i]=read(),sum[i]=sum[i-1]+b[i];
	for(int i=1; i<=n; ++i) {
		R[bl[i]=i/Len+1]=i;
		if(!L[bl[i]])L[bl[i]]=i;
	}
	for(int i=1; i<=bl[n]; ++i)Update(i);
	for(int i=1,op,l,r,x; i<=Q; ++i) {
		op=read(),l=read(),r=read();
		if(op==1) {
			x=read();
			if(bl[l]==bl[r]) {
				Down(bl[l]);
				for(int j=l; j<=r; ++j)a[j]+=x;
				Update(bl[l]);
			} else {
				Down(bl[l]),Down(bl[r]);
				for(int j=L[bl[r]]; j<=r; ++j)a[j]+=x;
				for(int j=R[bl[l]]; j>=l; --j)a[j]+=x;
				Update(bl[l]),Update(bl[r]);
				for(int j=bl[l]+1; j<bl[r]; ++j)tag[j]+=x;
			}
		} else {
			long long ll=-2e14,rr=2e14,mid,ans;
			while(ll<=rr) {
				mid=ll+rr>>1;
				if(Check(l,r,mid))ans=mid,rr=mid-1;
				else ll=mid+1;
			}
			if(bl[l]==bl[r]) {
				Down(bl[l]);
				for(int j=l; j<=r; ++j)a[j]=ans;
				Update(bl[l]);
			} else {
				Down(bl[l]),Down(bl[r]);
				for(int j=L[bl[r]]; j<=r; ++j)a[j]=ans;
				for(int j=R[bl[l]]; j>=l; --j)a[j]=ans;
				Update(bl[l]),Update(bl[r]);
				for(int j=bl[l]+1; j<bl[r]; ++j)bj[j]=ans,tag[j]=0;
			}
			cout<<ans<<"\n";
		}
	}
	return 0;
}