#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
#include <numeric>
#include <map>
#include <unordered_map>
#include <set>
#include <cstring>
#include <cmath>
#include <iomanip>
#include <cassert>
#include <random>
#include <cstdlib>

#define debug(x) std::cout << #x << " " << (x) << '\n';
#define pb push_back
#define mp std::make_pair
#define remax(a, b) a = std::max((a), (b));
#define remin(a, b) a = std::min((a), (b));

class FenwickTree {
private:
    std::vector<int64_t> data;

public:
    FenwickTree(int32_t n): data(n + 1, 0) {}

    void add(int32_t ind, int64_t v) {
        while(ind < data.size()) {
            data[ind] += v;
            ind += (ind & (-ind));
        }
    }

    int64_t get(int32_t ind) {
        int64_t res = 0;
        while(ind > 0) {
            res += data[ind];
            ind -= (ind & (-ind));
        }
        return res;
    }
};

struct Interval {
    int32_t l, len;
    int64_t val;

    Interval(int32_t _l, int32_t _len, int64_t _val): l(_l), len(_len), val(_val) {}

    bool operator<(const Interval &o) const {
        if(l != o.l) return l < o.l;
        else if(len != o.len) return len < o.len;
        else return val < o.val;
    }
};

void splitIntervals(std::set<Interval> &s, int32_t l, int32_t r) {
    auto it = s.lower_bound(Interval(l + 1, -1, 0));
    assert(it != s.begin());
    if(it != s.begin()) {
        it--;
        if(it->l != l) {
            auto i1 = Interval(it->l, l - it->l, it->val);
            auto i2 = Interval(l, it->len - (l - it->l), it->val);
            s.erase(it);
            s.insert(i1);
            s.insert(i2);
        }
    }

    it = s.lower_bound(Interval(r + 1, -1, 0));
    assert(it != s.begin());
    if(it != s.begin()) {
        it--;
        if(it->l + it->len != r + 1) {
            auto i1 = Interval(it->l, r - it->l + 1, it->val);
            auto i2 = Interval(r + 1, it->len - (r - it->l + 1), it->val);
            s.erase(it);
            s.insert(i1);
            s.insert(i2);
        }
    }
}

int main() {
#ifdef USEFOPEN
    freopen("1.in", "r", stdin);
    //freopen("1.out", "w", stdout);
#endif
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int32_t n, q;
    std::cin >> n >> q;

    std::vector<int32_t> a(n);
    for(int32_t i = 0; i < n; i++) {
        std::cin >> a[i];
    }

    std::vector<int64_t> b(n);
    for(int32_t i = 0; i < n; i++) {
        std::cin >> b[i];

        if(i != 0) {
            b[i] += b[i - 1];
        }
    }

    auto getIntervalB = [&b](int32_t l, int32_t r) {
        l--; r--;
        return b[r] - (l == 0 ? 0 : b[l - 1]);
    };

    auto check = [](int64_t middle, const std::vector<std::pair<int64_t, int64_t>> &x) {
        int64_t res = 0;
        for(int32_t i = 0; i < x.size(); i++) {
            res += abs(x[i].first - middle) * x[i].second;
        }
        return res;
    };

    std::set<Interval> s;
    s.insert(Interval(n + 1, 0, 0));
    s.insert(Interval(-1, 0, 0));
    for(int32_t i = 0; i < n; i++) {
        s.insert(Interval(i + 1, 1, a[i]));
    }

    FenwickTree fenwick(n);

    for(int32_t i = 0; i < q; i++) {
        int32_t type, l, r;
        std::cin >> type >> l >> r;

        if(type == 1) {
            int32_t x;
            std::cin >> x;

            fenwick.add(l, x);
            fenwick.add(r + 1, -x);

            splitIntervals(s, l, r);
        }
        else {
            splitIntervals(s, l, r);

            std::vector<std::pair<int64_t, int64_t>> x;
            auto it = s.lower_bound(Interval(l, -1, 0));
            std::set<int64_t> vals;
            while(it->l <= r) {
                int64_t prefSum = fenwick.get(it->l);
                fenwick.add(it->l, -prefSum);
                fenwick.add(it->l + it->len, prefSum);

                x.pb({ it->val + prefSum, getIntervalB(it->l, it->l + it->len - 1) });
                vals.insert(it->val + prefSum);

                auto jt = it;
                it++;

                s.erase(jt);
            }

            std::sort(x.begin(), x.end());
            std::vector<int64_t> values;
            for(auto x: vals)   values.push_back(x);

            int32_t low = 0, high = values.size() - 1;
            while(low < high) {
                int32_t mid = (low + high) / 2;

                //std::cout << mid << " " << check(mid, x) << " " << check(mid + 1, x) << '\n';
                if(check(values[mid], x) <= check(values[mid + 1], x)) {
                    high = mid;
                }
                else {
                    low = mid + 1;
                }
            }

            assert(low == high);
            std::cout << values[low] << '\n';

            s.insert(Interval(l, r - l + 1, values[low]));
        }

        /**
        for(auto &x : s) {
            std::cout << " { " << x.l << ", " << x.len << ", " << x.val << " }, ";
        }
        std::cout << '\n';
        */
    }
}