#include<bits/stdc++.h>
using db = double;
using std::cin;
using std::cout;
using cp = std::complex<db>;
using ll = long long;
const int N = 300005;
int n, q;
ll b[N];

int a[N];
std::set<int> set;
ll bit[N];
void add(int p, ll v) {
	for(;p < N;p += p & -p) {
		bit[p] += v;
	}
}
ll qpos(int p) {
	ll ans = 0;
	for(;p;p &= p - 1) ans += bit[p];
	return ans;
}

int main() {
	std::ios::sync_with_stdio(false), cin.tie(0);
	cin >> n >> q;
	for(int i = 1;i <= n;++i) {
		cin >> a[i], set.emplace(i);
		add(i, a[i] - a[i - 1]);
	}
	set.emplace(n + 1);
	for(int i = 1;i <= n;++i) cin >> b[i], b[i] += b[i - 1];
	for(int i = 1, op, l, r;i <= q;++i) {
		cin >> op >> l >> r;
		set.emplace(l);
		set.emplace(r + 1);
		if(op == 1) {
			int x;
			cin >> x;
			add(l, x);
			add(r + 1, -x);
		} else {
			auto iter = set.lower_bound(l);
			using pr = std::pair<ll, ll>;
			std::vector<pr> o;
			for(;*iter <= r;++iter) {
				int L = *iter, R = *next(iter) - 1;
				o.emplace_back(qpos(L), b[R] - b[L - 1]);
			}
			sort(o.begin(), o.end());
			ll sl = o[0].second, sr = 0;
			for(int i = 1;i < (int) o.size();++i) sr += o[i].second;
			int pos = 0;
			for(;pos + 1 < (int) o.size() && sl < sr;) {
				pos += 1;
				sl += o[pos].second;
				sr -= o[pos].second;
			}
			ll w = o[pos].first;
			cout << w << '\n';
			iter = set.lower_bound(l);
			for(;*iter <= r;iter = set.erase(iter)) {
				int L = *iter, R = *next(iter) - 1;
				ll add = w - qpos(L);
				::add(L, add);
				::add(R + 1, -add);
			}
			set.emplace(l);
			set.emplace(r + 1);
		}
	}
}