codeforces.com/contest/251/problem/C

C. Number Transformation

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Little Petya likes positive integers a lot. Recently his mom has presented him a positive integer a. There's only one thing Petya likes more than numbers: playing with little Masha. It turned out that Masha already has a positive integer b. Petya decided to turn his number a into the number b consecutively performing the operations of the following two types:

1. Subtract 1 from his number.
2. Choose any integer x from 2 to k, inclusive. Then subtract number (a mod x) from his number a. Operation a mod x means taking the remainder from division of number a by number x.

Petya performs one operation per second. Each time he chooses an operation to perform during the current move, no matter what kind of operations he has performed by that moment. In particular, this implies that he can perform the same operation any number of times in a row.

Now he wonders in what minimum number of seconds he could transform his number a into number b. Please note that numbers x in the operations of the second type are selected anew each time, independently of each other.

Input

The only line contains three integers a, b (1 ≤ b ≤ a ≤ 1018) and k (2 ≤ k ≤ 15).

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64dspecifier.

Output

Print a single integer — the required minimum number of seconds needed to transform number a into number b.

Examples

input

10 1 4

output

6

input

6 3 10

output

2

input

1000000000000000000 1 3

output

666666666666666667

Note

In the first sample the sequence of numbers that Petya gets as he tries to obtain number b is as follows: 10  →  8  →  6  →  4  →  3  →  2  →  1.

In the second sample one of the possible sequences is as follows: 6  →  4  →  3.

 题意：

给出 a b k

求a变到b的最小步数，每一步可以选择两种变化中的一种：a=a-1和a=a-a%i (2<=i<=k);

代码：

//k最大只有15，首先要想到2~15的lcm必然是一个循环节，然后就可以利用分块的思想，分成(a-1)/lcm+1块，每一块
//的大小是lcm,然后中间整个块的可以计算（每一块最大不会超过360360），两边的剩余的也可以计算了。这里我用的
//记忆化bfs找的。
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN=1000009;
int k,vis[MAXN];
int gcd_(int x,int y) { return y==0?x:gcd_(y,x%y); }
int lcm_(int x,int y) { return x/gcd_(x,y)*y; }
ll bfs(ll x,ll y)
{
    queue<ll>q;
    memset(vis,-1,sizeof(vis));
    q.push(x);
    vis[x-y]=0;
    while(!q.empty()){
        ll now=q.front();q.pop();
        if(now==y) return vis[0];
        for(int i=2;i<=k;i++){
            ll xx=now-now%i;
            if(xx<y||vis[xx-y]!=-1) continue;
            vis[xx-y]=vis[now-y]+1;
            q.push(xx);
        }
        ll xx=now-1;
        if(vis[xx-y]!=-1) continue;
        vis[xx-y]=vis[now-y]+1;
        q.push(xx);
    }
}
int main()
{
    ll a,b,ans=0;
    cin>>a>>b>>k;
    if(k==2){
        cout<<a-b<<"\n";
        return 0;
    }
    ll last=2;
    for(int i=3;i<=k;i++) last=lcm_(last,i);
    ll tmp1=a/last;
    ll tmp2=(b-1)/last+1;
    if(tmp1>tmp2) ans=bfs(a,tmp1*last)+(tmp1-tmp2)*bfs(last,0)+bfs(last*tmp2,b);
    else ans=bfs(a,b);
    cout<<ans<<"\n";
    return 0;
}