#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define pii pair<int,int>
#define piii tuple<int,int,int>
#define mp make_pair
#define mt make_tuple
#define x first
#define y second
#define fi first
#define se second
#define era erase
#define ins insert
#define it iterator
#define lb lower_bound
#define ub upper_bound
#define exc(exp) if(exp)continue;
#define ret(exp) if(exp)return;
#define stop(exp) if(exp)break;
#define quit(sth) {sth;return;}
#define let(var...) int var;tie(var)
#define siz(vec) ((int)((vec).size()))
#define all(vec) (vec).begin(),(vec).end()
#define unq(vec) sort(all(vec)),(vec).erase(unique(all(vec)),(vec).end())
#define deb(var) cerr<<#var<<'='<<(var)<<"; "
#define debl(var) cerr<<#var<<'='<<(var)<<";\n"
#define int long long
#define inf (long long)(1e18)
mt19937 gen(random_device{}());
void Max(int &x,int y){if(x<y)x=y;}
void Min(int &x,int y){if(x>y)x=y;}
const int mod=998244353;
void Add(int &x,int y){x=x+y<mod?x+y:x+y-mod;}
int add(int x,int y){return x+y<mod?x+y:x+y-mod;}
int fpm(int x,int y){
	int ans=1;for(;y;y>>=1,(x*=x)%=mod)if(y&1)(ans*=x)%=mod;return ans;
}

int n,a[500010],b[500010];

int cnt[500010];
bool chk(){
    fill(cnt,cnt+n+1,0);
    int al=0;
    for(int i=1;i<=n;i++)al+=!cnt[a[i]],++cnt[a[i]];
    fill(cnt,cnt+n+1,0);
    for(int i=1,j=0,c=0;i<=n;i++){
        while(j<=n&&c<al){
            ++j;
            c+=!(cnt[a[j]]++);
        }
        if(b[i]!=j)return 0;
        //return deb(i),deb(j),debl(b[i]),0;
        c-=!(--cnt[a[i]]);
    }                           return 1;
}
int fa[500010];
int find(int u){
    return fa[u]==u?u:fa[u]=find(fa[u]);
}
int lst[500010];
void work(){
    cin>>n;
    for(int i=1;i<=n;i++)cin>>b[i];b[n+1]=n+1;
    for(int i=1;i<=n;i++)
        if(b[i]<b[i-1])quit(cout<<"-1\n");
    
    fill(lst+1,lst+n+1,0);

    int LIM=n,CNT=1;
    for(int i=1;i<=n;i++)
        if(b[i]!=n+1)Min(LIM,b[i]-i+1);

    // debl(LIM);

    queue<int> q;
    for(int i=1;i<=n+1;i++){
        if(b[i]>b[i-1]){
            lst[b[i]]=i-1;
            for(int j=b[i-1]+1;j<b[i];j++){
                if(CNT<LIM)++CNT;
                else{
                    if(!q.empty())lst[j]=q.front(),q.pop();
                    else lst[j]=j-1;
                }
                if(b[j]==b[j+1])q.push(j);
            }
            if(b[b[i]]==b[b[i]+1])q.push(b[i]);
        }
    }
    for(int i=1,c=0;i<=n;i++){
        a[i]=lst[i]?a[lst[i]]:++c;
        // deb(i),cerr<<(a[i])<<'\n';
    }
    // cerr<<'\n';

    if(!chk())cout<<"-1\n";
    else{
        for(int i=1;i<=n;i++)cout<<a[i]<<" \n"[i==n];
    }
}
signed main(){
    // freopen("sing.in","r",stdin);
    // freopen("sing.out","w",stdout);
	ios::sync_with_stdio(0),
	cin.tie(0),cout.tie(0);
	int T=1;cin>>T;while(T--)work();
}
/*
 * CONTINUE, NON-STOPPING, FOR THE FAITH
 * START TYPING IF YOU DON'T KNOW WHAT TO DO
 * STOP TYPING IF YOU DON'T KNOW WHAT YOU'RE DOING
 */