#include <bits/stdc++.h>

using namespace std;

#define rep(i, s, e) for (int i = s; i <= e; ++i)
#define drep(i, s, e) for (int i = s; i >= e; --i)
#define file(a) freopen(#a".in", "r", stdin), freopen(#a".out", "w", stdout)
#define pv(a) cout << #a << " = " << a << endl
#define pa(a, l, r) cout << #a " : "; rep(_, l, r) cout << a[_] << ' '; cout << endl

const int N = 2e5 + 10;

int read() {
  int x = 0, f = 1; char c = getchar();
  for (; c < '0' || c > '9'; c = getchar()) if (c == '-') f = -1;
  for (; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - 48;
  return x * f;
}

int n, b[N], L[N], p[N], a[N], cnt, len, buc[N], tot;
bool tag[N];

void solve() {
  n = read(), cnt = 0, len = n;
  rep(i, 1, n) b[i] = read(), L[i] = 0, p[i] = -1, tag[i] = false;
  if (b[1] == n + 1) return printf("-1\n"), void();
  rep(i, 1, n) if (b[i] < i) return printf("-1\n"), void();
  rep(i, 1, n) if (b[i] <= n) len = min(len, b[i] - i + 1);
  rep(i, 0, n - 1) if (b[i] < b[i + 1]) {
    rep(j, b[i], b[i + 1] - 1) L[j] = i + 1;
    tag[i] = true, p[b[i + 1]] = i;
  }
  priority_queue <int, vector <int>, greater <int> > q;
  a[0] = cnt = 1;
  rep(i, 1, n) {
    if (~p[i]) a[i] = a[p[i]];
    else if (cnt < len) a[i] = ++ cnt;
    else {
      if (q.size() && L[i] <= q.top()) a[i] = a[q.top()], q.pop();
      else return printf("-1\n"), void();
    }
    // cout << "i, a[i] = " << i << ' ' << a[i] << endl;
    if (q.size() && q.top() < L[i]) return printf("-1\n"), void();
    if (!tag[i]) q.push(i);
  }
  tot = 0;
  rep(i, 1, len) buc[i] = 0;
  for (int i = 1, j = 0; i <= n; ++ i) {
    if (i > 1) tot -= -- buc[a[i - 1]] == 0;
    while (j <= n && tot < len) {
      if (++ j <= n) tot += ++ buc[a[j]] == 1;
      else break;
    }
    // cout << "i, j = " << i << ' ' << j << endl;
    if (b[i] != j) return printf("-1\n"), void();
  }
  rep(i, 1, n) printf("%d%c", a[i], " \n"[i == n]);
}

int main() {
  for (int tc = read(); tc; -- tc) {
    solve();
  }
  return 0;
}