#include<bits/stdc++.h>
using namespace std;
#pragma GCC optimize(3)
priority_queue<pair<int,int> ,vector<pair<int,int> >,greater<pair<int,int> > >q,qq;
int a[500005],b[500005],pre[500005],to[500005];
int n;
int c[500005];
bool check(){
	int tot = 0,cnt =0 ;
	for(int i = 0;i<=n;i++)c[i] = 0;
	for(int i = 1;i<=n;i++)if(!c[a[i]])++tot,c[a[i]] = 1;
	for(int i =0;i<=n;i++)c[i] = 0;
	int l = 0;
	for(int i = 1;i<=n;i++){
		if(i!=1){if(--c[a[i-1]]==0)--cnt;}
		while(l<min(b[i],n)){
			++l;++c[a[l]];
			if(c[a[l]] == 1)++cnt;
			if(l!=b[i] and cnt == tot)return 0;
		}
		if(cnt!=tot and b[i]!=n+1)return 0;
	}
	return 1;
}
void solve(){
	q=qq;
	cin >> n;
	for(int i = 1;i<=n;i++)pre[i] = 0,to[i] = 0;
	for(int i = 1;i<=n;i++)cin >> b[i];
	int mx =n;
	for(int i = 1;i<=n;i++)if(b[i]!=n+1)mx = min(mx,b[i]-i+1);
	if(b[1] == n+1 or mx <= 0){cout << "-1" << '\n';return;}
	if(mx == 1){
		int ok = 1;
		for(int i = 1;i<=n;i++)if(b[i]!=i)ok=0;
		if(!ok){cout << "-1" << '\n';return;}
		else {
			for(int i = 1;i<=n;i++)cout << 1 << " ";cout << '\n';
		}
		return;
	}
	for(int i = 1;i<n;i++){
		if(b[i]>b[i+1]){cout << "-1" << '\n';return;}
		if(b[i+1]!=b[i]){
			pre[b[i+1]] = i;
			to[i] = b[i+1];
		}
	}
	for(int i = 1;i<mx;i++)q.push({0,i});
	for(int i = 1;i<=n;i++){
		if(pre[i] or i == b[1]){
			if(pre[i])a[i] = a[pre[i]];
			else a[i] = mx;
		}else{
			if(q.empty()){cout << -1 << '\n';return;}
			assert(q.size());
			a[i] = q.top().second;q.pop();
		}
		if(!to[i])q.push({i,a[i]});
	}
	if(!check()){cout << -1 << '\n';}
	else{
		for(int i = 1;i<=n;i++)cout << a[i] << " ";
		cout << '\n';
	}
	return;
}
signed main(){
//	freopen("sing2.in","r",stdin);
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int t;cin >> t;
	while(t--)solve();
	return 0;
}/*
1
7
1 2 3 4 5 6 7
*/