You all know the Dirichlet principle, the point of which is that if n boxes have no less than n?+?1 items, that leads to the existence of a box in which there are at least two items.

Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a

Who loses if both players play optimally and Stas‘s turn is first?

Input

The only input line has three integers a,?b,?n (1?≤?a?≤?10000, 1?≤?b?≤?30, 2?≤?n?≤?10⁹) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n

Output

Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing".

Examples

2 2 10

Masha

5 5 16808

Masha

3 1 4

Stas

1 4 10

Missing

Note

In the second example the initial number of ways is equal to 3125.

• If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas‘s move will lead to defeat.
• But if Stas increases the number of items, then any Masha‘s move will be losing.

題意：（a+x）^（b+y）>n，輸出敗者

dfs遍歷每一種情況，遞歸到底之後回溯。

#include<bits/stdc++.h>  
using namespace std;  
#define ll long long  
bool kp(ll a,ll b,ll n)  
{  
    ll r=1;  
    while(b)  
    {  
        if(b&1)r=r*a;  
        if(r>=n||a>=n)return 0;  
        a=a*a;b=b/2;  
    }  
    return 1;  
}  
int dfs(ll a,ll b,ll n)//dfs(a,b,n)表示當參數為a,b,n時對於先手的狀態。  
{  
    bool k1=kp(a+1,b,n),k2=kp(a,b+1,n);  
    if(a==1&&!k1)return 2;//平局  
    if(k2&&!dfs(a,b+1,n))return 1;//把敗態轉移給對方  
    if(k1&&!dfs(a+1,b,n))return 1;//同上  
    if(k1&&dfs(a+1,b,n)==2)return 2;//無法把敗態轉移給對方但是可以維持平局  
    if(k2&&dfs(a,b+1,n)==2)return 2;//同上  
    return 0;//無論怎樣操作都把勝態留給對手  
}  
int main()  
{  
    ll a,b,n;scanf("%lld%lld%lld",&a,&b,&n);  
    int t=dfs(a,b,n);  
    if(t==1)printf("Masha\n");  
    else if(t==0)printf("Stas\n");  
    else printf("Missing\n");  
    return 0;  
}  

codeforce -39E-What Has Dirichlet Got to Do with That?(博弈+dfs)