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)

#include <bits/stdc++.h>
#define itn int
#define REP(i, n) for (ll i = 0; i < n; i++)
#define IREP(i, n) for (ll i = n - 1; i >= 0; i--)
#define FOR(a, b) for (ll i = a; i < b + 1; i++)
#define all(v) v.begin(), v.end()
using namespace std;
typedef long long ll;

const ll INF = 1LL << 60;
const ll MOD = 1000000007;
template<class T> inline bool chmin(T &a, T b){if (a > b){a = b;return true;}return false;}
template<class T> inline bool chmax(T &a, T b){if (a < b){a = b;return true;}return false;}

ll cmb(int n, int k)
{
    ll coef = 1;
    vector<ll> sieve(n + 1, 0);
    if (n < k)
    {
        coef = 0;
        return coef;
    }
    if (n == k || k == 0)
    {
        coef = 1;
        return coef;
    }
    k = min(k, n - k);
    for (ll p = 2; p <= n; p++)
    {
        if (sieve.at(p) == 0)
        {
            for (ll i = p * p; i <= n; i += p)
            {
                sieve.at(i) = 1;
            }
            for (ll prime = p; prime <= n; prime *= p)
            {
                ll cnt = n / prime - k / prime - (n - k) / prime;
                REP(j, cnt)
                {
                    coef *= p;
                    coef %= MOD;
                }
            }
        }
    }
    return coef;
}
int main(){
    string s;
    cin >> s;
    int k;
    cin >> k;
    int size=s.size();
    if(k==1){
        ll ans=9*(size-1)+(s[0]-'0');
        cout << ans << endl;
        return 0;
    }
    if(k==2){
        if(size==1){
            cout << 0 << endl;
            return 0;
        }
        ll ans = (s[1]-'0')+9*(size-2)+(s[0]-'0'-1)*9*(size-1);
        if(size>2){
            ans += cmb(size - 1, 2) * 9 * 9;
        }
        cout << ans << endl;
        return 0;
    }
    if(k==3){
        if(size<3){
            cout << 0 << endl;
            return 0;
        }
        ll ans = 9 * 9 * 9 * cmb(size - 1, 3) + (s[0] - '0') * (s[1] - '0') * (s[2] - '0')+(s[0]-'0')*(s[1]-'0')*9*(size-3)+(s[0]-'0')*9*9*cmb(size-1,2);
        if(size==3){
            ans = (s[0]-'0')*(s[1]-'0')*(s[2]-'0');
        }
        cout << ans << endl;
        return 0;
    }
}