the idea behind is just to choose the number for the ith place of the resulting string;

it changes every time that k is larger than factorial of the length of the remainder of the string (hope the code clarifies it a bit). I don't like string operations there, maybe there is something a bit more efficient? I tried swapping characters, but it's in fact slower

```
class Solution {
inline int fact(int i){
//i>=1&& i<=8 (since n<=9)
static int fact[]={1,2,6,24,120,720,5040,40320};
return fact[i-1];
}
public:
string getPermutation(int n, int k) {
k-=1;
string s;
for(int i=0;i<n;++i){
s.push_back('1'+i);
}
if(n==1) return s;
for(int i=0;i<n-1;++i){
int remLength=n-1-i; //always at least 1
int mod=fact(remLength);
int next=k/mod;
//s[i+next] is the value we want s[i] to have;
//s[i+1] should be what s[i] was, the remaining part should keep ordering
if(next!=0){
char tmp=s[i];
s[i]=s[i+next];
s.erase(s.begin()+i+next);
s.insert(s.begin()+i+1, tmp);
}
k%=mod;
}
return s;
}
};
```