Why the supply curve shifts rightwards when there is fall in input prices?

when the price of inputs fall it implies that the fall in the price of raw material and if the price of raw material fall it implies the fall in the cost pf prodution and if the cost is fall the the producer want to maximise the profit and due to this they increase their supply. pleaese note that there is no link of price of commodity. the point price of input is the part of other thing so dont compare it with price.