#include <bits/stdc++.h>   using namespace std;   int n;   pair<long long, long long> h2md_logl[100000][19];   pair<long long, long long> h2md_logr[100000][19];   long long dist_log[100000][19];   long long h[100000];   int max_2h_minus_d(int from, int to, int dir, long long& dist,                      long long& alldist) {     long long curd = 0;     long long dmark = 0;     long long curtree = from;     int curind = from;     int l = 0;     if (dir == 1) {       l = to - from;       if (l < 0) l += n;     } else if (dir == 0) {       l = from - to;       if (l < 0) l += n;     }     l++;     int l2 = 1;     int deg = 0;     while (l > 0) {       if (l % 2 == 1) {         pair<long long, long long> pret;         if (dir == 0)           pret = h2md_logl[curtree][deg];         else           pret = h2md_logr[curtree][deg];         long long dist_bw_marks = 0;         int newtree = curtree;         if (dir == 1) {           newtree += l2;           if (newtree >= n) newtree -= n;         } else {           newtree -= l2;           if (newtree < 0) newtree += n;         }         if (dir == 1)           dist_bw_marks = dist_log[curtree][deg];         else {           dist_bw_marks = dist_log[newtree][deg];         }         int pret_ind = pret.first;         if (pret.second - 2 * h[curind] - dmark > 0) {           dmark = dist_bw_marks + pret.second - 2 * h[pret_ind];           curind = pret_ind;         } else {           dmark += dist_bw_marks;         }         curtree = newtree;         curd += dist_bw_marks;       }       l /= 2;       l2 *= 2;       deg += 1;     }     dist = curd - dmark;     if (dir == 0)       alldist = curd - dist_log[curtree][0];     else {       curtree--;       if (curtree < 0) curtree += n;       alldist = curd - dist_log[curtree][0];     }     return curind;   }   int main() {     int m;     cin >> n >> m;     for (int i = 0; i < n; i++) {       cin >> dist_log[i][0];     }     for (int i = 0; i < n; i++) {       cin >> h[i];       h2md_logl[i][0] = make_pair(i, 2 * h[i]);       h2md_logr[i][0] = make_pair(i, 2 * h[i]);     }     int n2 = 2;     int deg = 1;     while (n2 < 2 * n) {       int half = n2 / 2;       for (int i = 0; i < n; i++) {         int mid = i + half;         int midl = i - half;         if (midl < 0) midl += n;         if (mid >= n) mid -= n;         long long disttohalf = dist_log[i][deg - 1];         long long disttohalfl = dist_log[midl][deg - 1];         dist_log[i][deg] = disttohalf + dist_log[mid][deg - 1];         if (h2md_logr[i][deg - 1].second >             h2md_logr[mid][deg - 1].second - disttohalf) {           h2md_logr[i][deg] = h2md_logr[i][deg - 1];         } else {           h2md_logr[i][deg] =               make_pair(h2md_logr[mid][deg - 1].first,                         h2md_logr[mid][deg - 1].second - disttohalf);         }         if (h2md_logl[i][deg - 1].second >             h2md_logl[midl][deg - 1].second - disttohalfl) {           h2md_logl[i][deg] = h2md_logl[i][deg - 1];         } else {           h2md_logl[i][deg] =               make_pair(h2md_logl[midl][deg - 1].first,                         h2md_logl[midl][deg - 1].second - disttohalfl);         }       }       deg++;       n2 *= 2;     }     long long distl, distr, alldist;     for (int i = 0; i < m; i++) {       int a, b;       cin >> a >> b;       int f, t;       f = b;       if (f >= n) f -= n;       t = a - 2;       if (t < 0) t += n;       int indf = max_2h_minus_d(f, t, 1, distl, alldist);       int indt = max_2h_minus_d(t, f, 0, distr, alldist);       if (indf != indt) {         cout << alldist + 2 * (h[indf] + h[indt]) - distl - distr;       } else if (indf == f) {         int newindt = indt + 1;         if (newindt == n) newindt = 0;         long long ndr, nar;         int indtt = max_2h_minus_d(t, newindt, 0, ndr, nar);         cout << alldist + 2 * (h[indf] + h[indtt]) - distl - ndr;       } else if (indt == t) {         int newindf = indf - 1;         if (newindf < 0) newindf = n - 1;         long long ndl, nal;         int indff = max_2h_minus_d(f, newindf, 1, ndl, nal);         cout << alldist + 2 * (h[indff] + h[indt]) - ndl - distr;       } else {         int newindf = indf - 1;         int newindt = indt + 1;         if (newindf < 0) newindf = n - 1;         if (newindt == n) newindt = 0;         long long ndl, ndr;         long long nal, nar;         int indff = max_2h_minus_d(f, newindf, 1, ndl, nal);         int indtt = max_2h_minus_d(t, newindt, 0, ndr, nar);         cout << max(alldist + 2 * (h[indff] + h[indt]) - ndl - distr,                     alldist + 2 * (h[indf] + h[indtt]) - distl - ndr);       }       cout << endl;     }     return 0;   }