Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

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

#include <bits/stdc++.h>
using namespace std;

#define int long long
const double PI = 3.14159265358979323846;
typedef vector<int> vint;
typedef pair<int, int> pint;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

typedef pair<int, int> P;

//ダイクストラ法を用いて単一始点最短路問題を解く
const int MAX_V = 110000;
const int INF = 1e12;

struct edge {
    int to, cost;
};

int V;
vector<edge> G[MAX_V];
int d[MAX_V];

void dijkstra(int s) {
    priority_queue<P, vector<P>, greater<P> > que;
    fill(d, d + V, INF);
    d[s] = 0;
    que.push(P(0, s));

    while (!que.empty()) {
        P p = que.top();
        que.pop();
        int v = p.second;
        if (d[v] < p.first)
            continue;
        for (int i = 0; i < G[v].size(); i++) {
            edge e = G[v][i];
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                que.push(P(d[e.to], e.to));
            }
        }
    }
}

int K;
signed main() {
    cin >> K;
    V = K;
    for (int i = 0; i < K; i++) {
        if (i % 10 != 9)G[i].push_back({(i + 1) % K, 1});
        G[i].push_back({i * 10 % K, 0});
    }
    dijkstra(1);
    cout << d[0] + 1 << endl;
}