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C. Parquet

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOnce Bob decided to lay a parquet floor in his living room. The living room is of size *n* × *m* metres. Bob had planks of three types: *a* planks 1 × 2 meters, *b* planks 2 × 1 meters, and *c* planks 2 × 2 meters. Help Bob find out, if it is possible to parquet the living room with such a set of planks, and if it is possible, find one of the possible ways to do so. Bob doesn't have to use all the planks.

Input

The first input line contains 5 space-separated integer numbers *n*, *m*, *a*, *b*, *c* (1 ≤ *n*, *m* ≤ 100, 0 ≤ *a*, *b*, *c* ≤ 10^{4}), *n* and *m* — the living room dimensions, *a*, *b* and *c* — amount of planks 1 × 2, 2 × 1 и 2 × 2 respectively. It's not allowed to turn the planks.

Output

If it is not possible to parquet the room with such a set of planks, output IMPOSSIBLE. Otherwise output one of the possible ways to parquet the room — output *n* lines with *m* lower-case Latin letters each. Two squares with common sides should contain the same letters, if they belong to one and the same plank, and different letters otherwise. Different planks can be marked with one and the same letter (see examples). If the answer is not unique, output any.

Examples

Input

2 6 2 2 1

Output

aabcca

aabdda

Input

1 1 100 100 100

Output

IMPOSSIBLE

Input

4 4 10 10 10

Output

aabb

aabb

bbaa

bbaa

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