import sys # sys.setrecursionlimit(1000005) # sys.set_int_max_str_digits(200005) int1 = lambda x: int(x)-1 pDB = lambda *x: print(*x, end="\n", file=sys.stderr) p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr) def II(): return int(sys.stdin.readline()) def LI(): return list(map(int, sys.stdin.readline().split())) def LLI(rows_number): return [LI() for _ in range(rows_number)] def LI1(): return list(map(int1, sys.stdin.readline().split())) def LLI1(rows_number): return [LI1() for _ in range(rows_number)] def SI(): return sys.stdin.readline().rstrip() dij = [(0, 1), (-1, 0), (0, -1), (1, 0)] # dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)] inf = -1-(-1 << 31) # inf = -1-(-1 << 63) # md = 10**9+7 md = 998244353 def solve(): def binary_search(l, r, minimize): if minimize: l -= 1 else: r += 1 while l+1 < r: m = (l+r)//2 if ok(m) ^ minimize: l = m else: r = m if minimize: return r return l def ok(m): return n-1+m=a[-1]: print(-1) else: d=binary_search(0,x,False) a[-1]-=d*(n-1) for i in range(n-1):a[i]+=d d=a[-1]-(a[-2]+2) if d>0: a[-1]-=d for i in range(n-2,n-2-d,-1):a[i]+=1 print(*a[::-1]) for _ in range(II()):solve()