#include <bits/stdc++.h>
using namespace std;
const long long ml = 3e5 + 101;
long long n, m, sum;
long long dis[ml], sa[ml], si[ml], h[ml];
long long ma[ml << 2], mi[ml << 2];
inline long long read() {
  long long r = 0, f = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) r = (r << 1) + (r << 3) + (c ^ 48), c = getchar();
  return r * f;
}
inline void write_down(long long x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write_down(x / 10);
  putchar(x % 10 + '0');
}
inline void port(long long x, char s) {
  write_down(x);
  putchar(s);
}
long long maxxx(long long x, long long y) { return sa[x] > sa[y] ? x : y; }
long long minnn(long long x, long long y) { return si[x] < si[y] ? x : y; }
void spread(long long x) {
  ma[x] = maxxx(ma[x << 1], ma[x << 1 | 1]);
  mi[x] = minnn(mi[x << 1], mi[x << 1 | 1]);
}
void build(long long l = 1, long long r = (n << 1 | 1), long long x = 1) {
  if (l == r) {
    ma[x] = mi[x] = l;
    return;
  }
  long long mid = (l + r) >> 1;
  build(l, mid, x << 1);
  build(mid + 1, r, x << 1 | 1);
  spread(x);
}
long long aska(long long ql, long long qr, long long x = 1, long long l = 1,
               long long r = (n << 1 | 1)) {
  if ((ql <= l) && (qr >= r)) return ma[x];
  long long mid = (l + r) >> 1, res = 0;
  if (ql <= mid) res = aska(ql, qr, x << 1, l, mid);
  if (qr > mid) res = maxxx(res, aska(ql, qr, x << 1 | 1, mid + 1, r));
  return res;
}
long long aski(long long ql, long long qr, long long x = 1, long long l = 1,
               long long r = (n << 1 | 1)) {
  if ((ql <= l) && (qr >= r)) return mi[x];
  long long mid = (l + r) >> 1, res = 0;
  if (ql <= mid) res = aski(ql, qr, x << 1, l, mid);
  if (qr > mid) res = minnn(res, aski(ql, qr, x << 1 | 1, mid + 1, r));
  return res;
}
long long reaski(long long l, long long r) {
  if (l > r) return 0;
  return aski(l, r);
}
long long reaska(long long l, long long r) {
  if (l > r) return 0;
  return aska(l, r);
}
long long solve(long long l, long long r) {
  long long mi = reaski(l, r), ma = reaska(l, r);
  if (mi != ma) return sa[ma] - si[mi];
  long long mi1 = minnn(reaski(l, mi - 1), reaski(mi + 1, r));
  long long ma1 = maxxx(reaska(l, mi - 1), reaska(mi + 1, r));
  return ((sa[ma1] - si[mi]) > (sa[ma] - si[mi1]) ? (sa[ma1] - si[mi])
                                                  : (sa[ma] - si[mi1]));
}
int main() {
  n = read(), m = read();
  for (long long i = 1; i <= n; i++)
    dis[i % n + 1] = dis[i % n + 1 + n] = read();
  for (long long i = 1; i <= n; i++) h[i] = h[i + n] = read();
  sa[0] = -1e15;
  si[0] = 1e15;
  for (long long i = 1; i <= (n << 1); i++) {
    sum += dis[i];
    sa[i] = sum + (h[i] << 1);
    si[i] = sum - (h[i] << 1);
  }
  build();
  while (m--) {
    long long l = read(), r = read();
    if (l <= r)
      port(solve(r + 1, l + n - 1), '\n');
    else
      port(solve(r + 1, l - 1), '\n');
  }
  return 0;
}
