Pebbles#1414

Pebbles

1 second
128 megabytes
Very easy

The Law of the Jungle clearly states that any wolf who starts a family may leave his Pack. However, once his cubs are grown and independent, he must present them to the Pack Council, which typically convenes once a month during the full moon, to introduce them to the other wolves.

Father Wolf waited patiently until his cubs were old enough to run a little. On one of those nights when the pack gathered, he brought the cubs, Mowgli, and Mother Wolf to the Council Rock. This was a hilltop, covered with large boulders where the entire pack could hide. Akela, the great gray lone wolf, chosen as the leader of the pack for his strength and agility, addressed the assembly from his rock:

— The law is known to you, the law is known to you! Look, wolves!

Father Wolf nudged little Frog, Mowgli, into the center of the circle. Mowgli sat on the ground, laughed, and began to play with the pebbles that sparkled in the moonlight. The game was as follows: He could move k_1,\, k_2,\, k_3,\, \ldots,\, k_n pebbles from one pile to another, and similarly could transfer k_1,\, k_2,\, k_3,\, \ldots,\, k_n pebbles from the second pile back to the first. He wondered if it was possible to obtain exactly pebbles in the second pile.

Input

The first line contains two integers and (2 \leq n \leq 1000, 2 \leq m \leq 2 \cdot 10^9). The second line contains natural numbers k_1,\, k_2,\, k_3,\, \ldots,\, k_n (k_i \leq 2 \cdot 10^9).

Output

Print YES if it is possible to have exactly pebbles in the second pile, and NO otherwise.

Examples

Example 1

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