CF615D Multipliers

Ayrat has number $ n $ , represented as it's prime factorization $ p_{i} $ of size $ m $ , i.e. $ n=p_{1}·p_{2}·...·p_{m} $ . Ayrat got secret information that that the product of all divisors of $ n $ taken modulo $ 10^{9}+7 $ is the password to the secret data base. Now he wants to calculate this value.

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In the first sample $ n=2·3=6 $ . The divisors of $ 6 $ are $ 1 $ , $ 2 $ , $ 3 $ and $ 6 $ , their product is equal to $ 1·2·3·6=36 $ . In the second sample $ 2·3·2=12 $ . The divisors of $ 12 $ are $ 1 $ , $ 2 $ , $ 3 $ , $ 4 $ , $ 6 $ and $ 12 $ . $ 1·2·3·4·6·12=1728 $ .