已AC但疑惑

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

vector<int> a[100010];
int ans,n,d,x,y;

void dfs(int x,int sum){
	if(sum>d) return;
	ans++;
	for(int i=0;i<=a[x].size()-1;i++){
		int k=a[x][i];
		dfs(k,sum+1);
	}
}
void youhua(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
}
signed main(){
    youhua();
    cin>>n>>d;
	for(int i=1;i<=n-1;i++){
		cin>>x>>y;
		a[x].push_back(y);
	}
	dfs(1,0);
	cout<<ans-1;	
    return 0;
}

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

vector<int> a[100010];
int ans,n,d,x,y;
bool v[100010];
void dfs(int x,int sum){
	if(x>n) return;
	if(sum>d) return;
	ans++;
	for(int i=0;i<=a[x].size()-1;i++){
		int k=a[x][i];
		if(!v[k])
			dfs(k,sum+1),v[k]=true;
	}
}
void youhua(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
}
signed main(){
    youhua();
    cin>>n>>d;
	for(int i=1;i<=n-1;i++){
		cin>>x>>y;
		a[x].push_back(y);
		a[y].push_back(x);
	}
	dfs(1,0);
	cout<<ans-1;	
    return 0;
}