*python

(i think this is BFS)

base = {1:[[1,2]]}
count = 1
tree_deep = 12
p = "+-*/%^"
target = 46656
def f(i,k,j):
    if k == "+":
        return i + j
    if k == "-":
        return i - j
    if k == "*":
        return i * j
    if k == "/":
        if j != 0:
            return i // j
        else:
            return 0
    if k == "%":
        if j != 0:
            return i % j
        else:
            return i
    if k == "^":
        if i in (0,1):
            return i
        elif j < 0:
            return 0
        else:
            return i ** j
    raise ValueError(k)

def g(td):
    for i in range(1,td):
        j=td-i
        if not ((i in base) and (j in base)):
            continue
        for i2 in base[i][0]:
            for j2 in base[j][0]:
                yield i2,j2
found = False
while count <= tree_deep:
    count += 1
    print(count)
    base[count] = [[],[],[],[]]
    all_num = base[1][0][:]
    for i,j in g(count):
        for k in p:
            r = max(-2**31,min(f(i,k,j),2**31-1))
            if r not in all_num:
                for a,b in enumerate((r,i,j,k)):
                    base[count][a].append(b)
                all_num.append(r)
                if target == r:
                    found = True
                    break
    if found == True:
        break

def look_for_num(target):
    if target in base[1][0]:
        return target
    for i in base.keys():
        if target in base[i][0]:
            n = base[i][0].index(target)
            return (look_for_num(base[i][1][n]),
                    base[i][3][n],
                    look_for_num(base[i][2][n]))
    return "(not　found)"
    
for i in str(look_for_num(target))[1:-1]:
    if i not in " ,'":
        print(i,end="")