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const int maxn = 40000 + 5;
const int T = 800 + 5;
int f[T][T];
int n, m, t;
int a[maxn], b[maxn];
int ct[maxn];
vector<int> show[maxn];
map<int, int> loc;
class Seg {
public:
int l, r;
};
Seg seg[maxn];
int pos[maxn];
void init() {
Set(pos, 0);
Set(f, 0);
_for(i, 0, maxn) show[i].clear();
Set(ct, 0);
loc.clear();
}
void discrete() {
sort(b + 1, b + 1 + n);
int tot = unique(b + 1, b + 1 + n) - b - 1;
_rep(i, 1, n) {
a[i] = lower_bound(b + 1, b + 1 + tot, a[i]) - b;
show[a[i]].push_back(i);
}
}
void split(const int len) {
_rep(i, 1, t) {
seg[i].l = (i - 1) * len + 1;
seg[i].r = i * len;
}
if(seg[t].r < n) {
t++;
seg[t].l = seg[t - 1].r + 1;
seg[t].r = n;
}
_rep(i, 1, n) {
_rep(j, seg[i].l, seg[i].r) pos[j] = i;
}
}
inline void cal() {
_rep(i, 1, t) {
int ans = 0, cnt = 0;
Set(ct, 0);
_rep(j, seg[i].l, n) {
ct[a[j]]++;
if(cnt < ct[a[j]] || (cnt == ct[a[j]] && a[j] < ans)) {
cnt = ct[a[j]];
ans = a[j];
}
f[i][pos[j]] = ans;
}
}
}
int count(int x, int l, int r) {
return upper_bound(show[x].begin(), show[x].end(), r) - lower_bound(show[x].begin(), show[x].end(), l);
}
void update(int x, int l, int r, int &ans, int &cnt) {
int c = count(x, l, r);
if(c > cnt || (c == cnt && x < ans)) {
cnt = c;
ans = x;
}
}
int ask(int l, int r) {
int p = pos[l], q = pos[r];
int ans = 0, cnt = 0;
if(p == q) {
_rep(i, l, r) update(a[i], l, r, ans, cnt);
return b[ans];
}
int x = 0, y = 0;
if(p + 1 <= q - 1) {
x = p + 1;
y = q - 1;
}
_rep(i, l, seg[p].r) update(a[i], l, r, ans, cnt);
_rep(i, seg[q].l, r) update(a[i], l, r, ans, cnt);
if(f[x][y]) update(f[x][y], l, r, ans, cnt);
//debug(ans);
return b[ans];
}
int main() {
freopen("input.txt", "r", stdin);
init();
cin >> n >> m;
_rep(i, 1, n) scanf("%d", &a[i]);
Cpy(b, a);
// == discrete ==
discrete();
// == discrete finished ==
// == part ==
t = sqrt(n * log(n) / log(2));
int len = t ? n / t : n;
// == split ==
split(len);
// == split finished ==
// == calculate f() ==
cal();
// == f() finished==
// == main algorithm ==
int res = 0;
while (m--) {
int l, r;
scanf("%d%d", &l, &r);
l = (l + res - 1) % n + 1;
r = (r + res - 1) % n + 1;
//debug(l), debug(r);
if(l > r) swap(l, r);
res = ask(l, r);
printf("%d\n", res);
}
}
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