E with SegTree

#include <bits/stdc++.h>
// tiom4eg's precompiler options
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
// IO settings
#define fastIO ios_base::sync_with_stdio(false); cin.tie(0)
// Quick types
#define ll long long
#define ld long double
#define ull unsigned long long
#define pii pair <int, int>
#define pll pair <ll, ll>
#define vi vector <int>
#define mi vector <vector <int> >
// Quick functions
#define endl "\n"
#define F first
#define S second
#define all(a) a.begin(), a.end()
#define pb push_back
#define mp make_pair
#define fint(n) int n; cin >> n
#define fstr(s) string s; cin >> s
#define farr(a, n) int a[n]; for (int pog = 0; pog < n; ++pog) cin >> a[pog]
#define min(a, b) ((a < b) ? (a) : (b))
#define max(a, b) ((a > b) ? (a) : (b))
// Quick fors
#define FOR1(s, n) for (int i = s; i < n; ++i)
#define FOR2(s, n) for (int j = s; j < n; ++j)
#define FOR3(s, n) for (int k = s; k < n; ++k)
#define RFOR(n, s) for (int l = n; l >= s; --l)
// Pragmas
#pragma GCC optimize("Ofast") // let the chaos begin!
#pragma GCC optimize ("unroll-loops")
#pragma target("avx,fma")
#pragma comment(linker, "/stack:200000000")
#pragma target("tune=native")
// PBDS
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree <int, null_type, less <int>, rb_tree_tag, tree_order_statistics_node_update>
#define ook order_of_key
#define fbo find_by_order
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
using namespace std;
using namespace __gnu_pbds;
mt19937 rng(std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now().time_since_epoch()).count());

const int R = 1 << 18;
int a[2 * R];

void build() { for (int i = R - 1; i >= 1; --i) a[i] = max(a[2 * i], a[2 * i + 1]); }

int get(int ql, int val, int node = 1, int nl = 0, int nr = R) {
    if (ql >= nr || a[node] < val) return -1;
    if (nl + 1 == nr && a[R + nl] >= val) return nl;
    int nm = (nl + nr) / 2;
    int lres = get(ql, val, 2 * node, nl, nm);
    if (lres >= 0) return lres;
    else return get(ql, val, 2 * node + 1, nm, nr);
}

int main() {
    fastIO;
    string s; cin >> s;
    int n = s.size();
    int k; cin >> k;
    FOR1(0, n) a[R + i] = s[i] - '0';
    build();
    string t;
    int pos = 0;
    while (pos < n) {
        int b = get(pos + 1, s[pos] - '0' + 1);
        if (b == -1 || b - pos > k) {
            t += s[pos];
            pos++;
        }
        else k -= (b - pos), pos = b;
    }
    int m = t.size();
    FOR1(0, m - k) cout << t[i];
}