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| #include <bits/stdc++.h>
using namespace std;
const double eps = 1e-10; const double pi = 3.1415926535897932384626433832795; const double eln = 2.718281828459045235360287471352;
#define f(i, a, b) for (int i = a; i <= b; i++) #define scan(x) scanf("%d", &x) #define mp make_pair #define pb push_back #define lowbit(x) (x&(-x))
#define fi first #define se second #define SZ(x) int((x).size()) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define summ(a) (accumulate(all(a), 0ll))
typedef unsigned long long ull; typedef pair<int,int> pii; typedef vector<int> vi;
using ll=long long;
ll tt,n,k,fa[(int)2e5+9],cnt; vi g[(int)2e5+9];
ll dfs(int u,int fa,int dep,ll x){ ll res=0; for(auto it:g[u]){ res=max(dfs(it,u,dep+1,x),res); } res+=1; if(res>=x&&fa!=1)cnt+=1,res=0; return res; }
bool check(ll x){ cnt=0; dfs(1,1,0,x); return cnt<=k; }
void solve(){ cin>>n>>k; for(int i=1;i<=n;++i)g[i].clear(); for(int i=2;i<=n;++i)cin>>fa[i],g[fa[i]].push_back(i); ll l=1,r=n-1; while(l<r){ ll mid=(l+r)>>1; if(check(mid))r=mid; else l=mid+1; } cout<<l<<'\n'; }
int main() { ios::sync_with_stdio(false); cin.tie(0); cin>>tt; f(sb,1,tt)solve(); return 0; }
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