#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"


void solve(){
    int n, q; in(n,q);
    vector<ll> a(n), b(n); in(a,b);
    vector<int> ts(n,0);
    int sz = bit_ceil<uint>(q);
    vector<vector<pil>> dat(sz*2);
    auto apply = [&](int l, int r, pil val){
        l += sz;
        r += sz;
        while (l < r){
            if (l & 1) dat[l++].emplace_back(val);
            if (r & 1) dat[--r].emplace_back(val);
            l >>= 1;
            r >>= 1;
        }
    };
    vector<int> ks(q);
    rep(i,q){
        int p, x, k; in(p,x,k); p--; k -= 2;
        apply(ts[p],i,pil(p,a[p]));
        a[p] = x;
        ts[p] = i;
        ks[i] = k;
    }
    rep(i,n){
        apply(ts[i],q,pil(i,a[i]));
    }
    vector<ll> ans(q,linf);
    auto proc = [&](int p, int ql, int qr){
        chmax(ql, 0);
        chmin(qr, q);
        if (ql >= qr) return ;
        vector<int> qids(qr - ql); iota(all(qids),ql);
        sort(all(qids),[&](int l, int r){
            return ks[l] < ks[r];
        });
        vector<int> iks; iks.reserve(qr - ql);
        for (int l = 0, r = 0; l < qr - ql; l = r){
            while (r < qr - ql && ks[qids[l]] == ks[qids[r]]) r++;
            iks.emplace_back(ks[qids[l]]);
        }
        int h = iks.size();
        sort(all(dat[p]));
        // out(p,ql,qr);
        // out(dat[p]);
        // out();
        int w = dat[p].size();
        auto f = [&](int i, int j){
            int k = iks[i];
            int aid = dat[p][j].first;
            int bid = k - aid;
            if (0 <= bid && bid < n) return b[bid] + dat[p][j].second;
            return linf;
        };
        vector<ll> ians(h,linf);
        auto dfs = [&](auto sfs, int lx, int rx, int ly, int ry) -> void {
            if (rx - lx <= 0) return ;
            if (ry - ly <= 0) return ;
            int mx = (lx + rx) / 2;
            pli mi(linf+1,-1);
            repp(j,ly,ry){
                chmin(mi,pli(f(mx,j),j));
            }
            ians[mx] = mi.first;
            sfs(sfs,lx,mx,ly,mi.second+1);
            sfs(sfs,mx+1,rx,mi.second,ry);
        };
        dfs(dfs,0,h,0,w);
        for (int l = 0, r = 0, id = 0; l < qr - ql; l = r, id++){
            while (r < qr - ql && ks[qids[l]] == ks[qids[r]]){
                chmin(ans[qids[r]],ians[id]);
                r++;
            }
        }
    };
    for (int d2 = 1; d2 <= sz; d2 <<= 1){
        int len = sz / d2;
        for (int p = d2, l = 0, r = len; p < d2*2; p++, l += len, r += len){
            proc(p, l, r);
        }
    }
    rep(i,q) out(ans[i]);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}