tensorflow: Error in gradient of reduce_prod

vars = tf.Variable([1., 2.])
tf.initialize_all_variables().run()
tf.gradients(tf.reduce_prod(vars), vars)[0].eval()

yields [ 2., 1.] which is correct. But

vars = tf.Variable([0., 2.])
tf.initialize_all_variables().run()
tf.gradients(tf.reduce_prod(vars), vars)[0].eval()

yields [ nan, 0.] which is incorrect. The correct gradient is [ 2., 0.]