Problem:
Score : 500 points

Problem Statement

Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.

Constraints

1 \leq N < 10^{100}

1 \leq K \leq 3

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the count.

Sample Input 1

100
1

Sample Output 1

19

The following 19 integers satisfy the condition:

1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100

Sample Input 2

25
2

Sample Output 2

14

The following 14 integers satisfy the condition:

11,12,13,14,15,16,17,18,19,21,22,23,24,25

Sample Input 3

314159
2

Sample Output 3

937

Sample Input 4

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3

Sample Output 4

117879300

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// ~maqsat~

// #pragma GCC target ("avx2")
// #pragma GCC optimize ("Ofast")
// #pragma GCC optimize ("unroll-loops")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>

#define F first
#define S second
#define in insert
#define pb push_back
#define eb emplace_back
#define sz(x) int(x.size())
#define all(x) x.begin(), x.end()
#define count1 __builtin_popcountl
#define debug(x) cerr << (#x) << " = " << (x) << "\n"
#define ACCELERATE ios_base::sync_with_stdio(false),cin.tie(nullptr)
#define fre(f) if(fopen(f".in", "r")) freopen(f".in", "r", stdin),freopen(f".out", "w", stdout)
#define ever ;;

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

using ll = long long;
using ull = unsigned long long;
// using big = __int128_t; // -10^38...10^38
using db = double;
using ld = long double;
typedef pair<int,int> ii;
typedef pair<ll,ll> pll;

template <class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <class T> inline void cmin(T &a, T b) { a = min(a, b); }
template <class T> inline void cmax(T &a, T b) { a = max(a, b); }

const int oo = 0x3f3f3f3f;
const ll N = 2e5 + 123;
const ll MOD = 1e9 + 7;
const ll INF = 1e15 + 9;
const db EPS = 1e-9;
const db PI = acos(-1); // 3.14159265358979323846
const int dx[] = {1, -1, 0, 0, 1, 1, -1, -1};
const int dy[] = {0, 0, 1, -1, 1, -1, -1, 1};

main() {
#ifdef ZVER
	cerr << "Ready\n";
#endif
	fre("");
	ACCELERATE;
	
	string s;
	cin >> s;
	
	int k;
	cin >> k;
	
	if (k == 1) {
		ll ans = 0;
		for (int i = 0; i < sz(s); i++) {
			if (!i) ans += s[i] - '0';
			else ans += 9;
		}
		cout << ans;
	}
	else if (k == 2) {
		ll ans = 0;
		for (int i = 0; i < sz(s); i++) {
			for (int j = i + 1; j < sz(s); j++) {
				if (!i) {
					ans += (s[i] - '0' - 1) * 9;
					if (j == 1) ans += s[j] - '0';
					else ans += 9;
				}
				else ans += 81;
			}
		}
		cout << ans;
	}
	else {
		ll ans = 0;
		for (int i = 0; i < sz(s); i++) {
			for (int j = i + 1; j < sz(s); j++) {
				for (int ii = j + 1; ii < sz(s); ii++) {
					if (!i) {
						ans += (s[i] - '0' - 1) * 81;
						if (j == 1) {
							ans += (s[j] - '0' - 1) * 9;
							if (ii == 2) ans += s[ii] - '0';
							else ans += 9;
						}
						else ans += 81;
					}
					else ans += 9 * 81;
				}
			}
		}
		cout << ans;
	}
	
	return 0;
}