Minimum Difference の 传送门
不显然不同出现次数的数最多 \(O \left ( \sqrt n \right )\)。
\(\sum\limits_{i=1}^k i = n\)
算出 \(k\) 最大为 \(\sqrt n\)。
则莫队 + 值域分块，维护每个出现次数有几个数。
查询时扫所有块，块内有值就暴力整块，把所有有值的位置提出来，做双指针。
具体一点，设当前双指针的左右端点分别为 \(l, r\)。
不断循环直到 \(\left [ l, r \right ]\) 总的出现次数大于等于 \(k\)。
然后每次把 \(l\) 往后移一位就行。
#include <bits/stdc++.h>
using namespace std;
inline int read()
{int f = 0, ans = 0;char c = getchar();while (!isdigit(c))f |= c == '-', c = getchar();while (isdigit(c))ans = (ans << 3) + (ans << 1) + c - 48, c = getchar();return f ? -ans : ans;
}
void write(int x)
{if (x < 0)putchar('-'), x = -x;if (x > 9)write(x / 10);putchar(x % 10 + '0');
}
constexpr int N = 1e5 + 5, V = 1e5, inf = 1e9;
int n, m, a[N], res[N];
int blk, l, r, bl[N], mp[N];
struct oper
{int p, lst, x;
} op[N];
struct quest
{int l, r, k, tim, id;bool operator<(const quest &rhs) const{if (bl[l] != bl[rhs.l])return l < rhs.l;if (bl[r] != bl[rhs.r])return r < rhs.r;return tim < rhs.tim;}
} q[N];
namespace block
{int blk, tot, bl[N], L[N], R[N];int t, s[N], cnt[N], cnt_blk[N];inline void init(){blk = pow(V, 2.0 / 3);tot = V / blk + (bool)(V % blk);for (int i = 1; i <= V; ++i)bl[i] = (i - 1) / blk + 1;for (int i = 1; i <= tot; ++i)L[i] = (i - 1) * blk + 1, R[i] = i * blk;R[tot] = V;}inline void modify(int x, int w) { x ? (cnt[x] += w, cnt_blk[bl[x]] += w) : 0; }inline int get_ans(int k){t = 0;for (int i = 1; i <= tot; ++i)if (cnt_blk[i])for (int j = L[i]; j <= R[i]; ++j)if (cnt[j])s[++t] = j;int ans = inf, sum = 0;for (int l = 1, r = 0; l <= t; ++l){while (r < t && sum < k)sum += cnt[s[++r]];if (sum < k)break;ans = min(ans, s[r] - s[l]);sum -= cnt[s[l]];}return ans;}
}
inline void init()
{block::init(), blk = pow(n, 2.0 / 3);for (int i = 1; i <= n; ++i)bl[i] = (i - 1) / blk + 1;
}
inline void insert(int x) { block::modify(mp[x], -1), block::modify(++mp[x], 1); }
inline void remove(int x) { block::modify(mp[x], -1), block::modify(--mp[x], 1); }
inline void insert_in_bound(int i)
{if (i >= l && i <= r)block::modify(mp[a[i]], -1), block::modify(++mp[a[i]], 1);
}
inline void remove_in_bound(int i)
{if (i >= l && i <= r)block::modify(mp[a[i]], -1), block::modify(--mp[a[i]], 1);
}
inline void forward(int i)
{auto &[p, lst, x] = op[i];remove_in_bound(p);a[p] = x;insert_in_bound(p);
}
inline void backward(int i)
{auto &[p, lst, x] = op[i];remove_in_bound(p);a[p] = lst;insert_in_bound(p);
}
signed main()
{// freopen("chk.in", "r", stdin);// freopen("chk.out", "w", stdout);n = read(), m = read();for (int i = 1; i <= n; ++i)a[i] = read();init();int que = 0, ti = 0;for (int i = 1; i <= m; ++i)if (read() == 1){++que, q[que] = {0, 0, 0, ti, que};q[que].l = read(), q[que].r = read(), q[que].k = read();}else{++ti;op[ti].lst = a[op[ti].p = read()];a[op[ti].p] = op[ti].x = read();}while (ti)a[op[ti].p] = op[ti].lst, --ti;sort(q + 1, q + que + 1);l = 1, r = 0;for (int i = 1; i <= que; ++i){while (l > q[i].l)insert(a[--l]);while (r < q[i].r)insert(a[++r]);while (l < q[i].l)remove(a[l++]);while (r > q[i].r)remove(a[r--]);while (ti < q[i].tim)forward(++ti);while (ti > q[i].tim)backward(ti--);res[q[i].id] = block::get_ans(q[i].k);}for (int i = 1; i <= que; ++i)write(res[i] == inf ? -1 : res[i]), putchar('\n');return 0;
}
