P17753 [HackerEarth] After giving the ideal bouquet to his crush Chotu now plans to propose his crush.
普及-
题目描述

After giving the ideal bouquet to his crush Chotu now plans to propose his crush.

Now the task is to say the right words. Chotu has four components (“aa”, “bb”, “ab”, “ba”) and he has to create the vow using these four components.

Chotu’s crush being an IIITian (Coder obviously) has an obsession for palindromic strings. She will only agree to the proposal if the vows are palindromic. Chotu being unknown to the world of palindromes ask you to help him creating the longest palindromic vow. Chotu gives you the count of each component (Caa, Cbb, Cab, Cba). If multiple palindromic vows exist than print lexicographically smallest vow.

Note

A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward. For eg. "abcba" is a palindrome but "abca" is not a palindrome. Empty string is also a palindrome.

Strings a1a2a3a4...an is said to be lexicographically smaller than b1b2b3b4...bn if for some i, a1 = b1, a2 = b2 ... ai-1 = bi-1 and ai < bi

Input

First line contains an integer T denoting number of test cases.

Next T lines contains four integers Caa, Cbb, Cab, Cba denoting the count of string "aa", "bb", "ab" and "ba" respectively.

Output

For each test case print the required string. It is guaranteed that from given input a non empty palindromic string can be formed.

Constraints

1 ≤ T ≤ 500

1 ≤ Caa + Cbb + Cab + Cba ≤ 2000

SAMPLE INPUT
4
2 1 0 0
1 1 0 0
3 2 1 1
3 2 1 0

SAMPLE OUTPUT
aabbaa
aa
aaabbbaabbbaaa
aabbaabbaa

Explanation

In the first sample test case the possible palindromic strings are {"aa", "bb", "aaaa", "aabbaa"}, but the longest palindromic string formed is "aabbaa".

In the second test case the possible palindromic strings are {"aa", "bb"} the answer is "aa" as there are two palindromic strings of size two, we will print the lexicographically smallest string.

输入格式

见题面

输出格式

见题面

样例输入
500 354 131 67 102 472 124 49 363 473 252 482 49 487 391 78 250 438 212 107 460 261 239 366 322 374 379 235 415 144 149 144 309 152 59 107 371 54 212 355 490 350 493 201 264 343 48 112 111 54 68 261 392 26 193 107 315 442 148 390 474 27 45 74 485 312 176 35 497 491 414 314 399 127 320 130 426 255 153 80 35 464 376 224 18 349 208 369 314 485 407 399 253 362 297 158 124 81 429 126 235 403 488 461 369 262 349 417 87 419 113 451 79 262 77 330 179 390 460 440 74 427 76 49 274 234 343 270 410 368 251 313 250 452 63 373 169 109 413 293 10 307 168 196 287 474 325 72 93 122 261 147 412 85 364 249 202 37 261 212 285 44 288 148 114 420 136 94 322 484 290 343 332 472 158 257 262 16 493 294 152 24 487 288 363 6 157 28 412 213 117 329 210 373 369 35 38 327 461 172 413 361 210 307 61 473 487 344 96 267 133 228 424 461 114 393 255 94 25 68 349 245 153 432 176 315 38 230 374 271 468 123 282 414 383 241 380 487 391 370 174 35 281 189 311 36 182 463 442 22 286 369 168 430 171 71 229 27 324 412 420 166 344 234 292 475 203 393 149 465 474 19 136 288 458 151 164 201 331 306 66 317 210 321 130 375 273 296 369 324 201 42 37 236 412 263 64 338 313 290 66 135 405 479 413 191 94 400 469 184 301 162 259 471 280 162 170 232 426 164 157 450 94 40 72 211 62 468 45 157 268 386 268 73 450 137 230 103 375 149 355 26 129 310 214 405 427 289 365 234 198 431 213 346 412 142 203 209 13 114 404 119 146 483 270 132 442 423 262 8 163 194 357 78 253 464 110 466 301 414 431 120 221 161 144 111 278 436 54 49 353 164 100 1 434 5 257 243 82 463 282 391 308 450 383 236 106 374 421 430 265 173 259 478 227 82 47 273 495 165 122 204 466 392 350 42 104 498 292 150 96 426 318 359 373 455 287 441 293 29 140 234 399 18 77 172 12 229 345 325 85 427 311 385 336 232 197 178 344 357 109 338 118 144 153 484 333 363 23 248 445 152 289 44 463 288 363 147 204 339 487 149 51 436 396 384 47 198 370 237 254 97 48 406 74 292 96 498 186 183 223 185 329 205 412 154 469 444 122 122 67 420 140 96 113 261 365 305 247 232 461 280 222 391 162 266 494 212 246 62 107 79 428 129 243 150 77 320 109 298 113 166 161 216 69 135 403 126 276 29 185 14 49 490 48 459 339 339 237 14 460 31 256 298 281 267 118 421 107 189 60 318 194 85 110 439 258 240 305 302 162 15 439 34 203 16 249 445 142 355 495 47 117 190 205 442 104 63 181 488 118 409 444 288 365 305 443 72 214 274 151 254 130 35 190 442 318 433 55 76 44 165 60 395 158 482 46 33 122 61 298 255 19 216 102 147 303 26 214 68 6 262 257 263 494 370 415 200 279 477 147 238 156 318 288 414 242 47 319 144 205 350 128 168 170 115 91 189 288 259 81 384 189 190 119 495 442 415 224 466 261 80 458 397 231 20 367 159 322 221 477 271 129 329 163 137 294 465 145 56 311 60 298 477 380 477 449 6 71 74 295 136 465 103 330 374 429 214 121 227 142 465 222 262 273 443 263 80 68 358 254 281 469 65 455 278 414 196 443 170 349 332 98 148 78 333 361 413 49 193 170 147 201 238 243 316 230 179 353 147 495 47 84 284 497 418 434 486 456 353 210 14 419 216 279 137 386 218 57 74 299 255 198 253 24 125 140 255 428 105 187 227 68 211 289 32 76 112 293 0 158 183 144 417 66 66 241 242 122 438 180 304 296 50 25 313 426 172 230 17 274 101 354 211 302 458 468 454 257 183 79 261 463 278 19 380 213 499 24 340 84 298 437 404 28 234 267 369 444 89 347 431 476 56 78 497 274 325 436 259 465 209 244 409 71 195 357 291 461 246 463 79 324 298 20 330 390 346 409 463 477 12 205 409 456 473 112 179 12 274 227 309 300 84 268 356 243 417 436 121 281 279 496 307 417 400 264 354 419 130 265 376 110 39 35 250 271 96 38 126 139 236 52 356 37 11 35 482 459 124 406 464 54 150 158 411 0 194 63 136 94 214 449 88 487 396 16 376 392 18 346 210 35 28 375 238 57 239 225 438 258 157 441 66 32 492 49 445 429 231 416 491 232 235 207 155 43 306 278 289 388 142 282 3 70 400 108 409 415 326 82 345 437 14 392 492 178 444 137 303 387 260 379 285 93 175 353 29 471 82 164 418 10 380 232 385 169 295 111 483 272 379 486 327 352 198 363 462 293 495 187 46 10 383 153 304 308 29 262 469 218 303 234 7 180 261 375 399 19 86 460 118 499 311 381 244 78 294 138 280 352 407 329 5 31 243 420 153 418 98 213 204 25 441 32 187 426 52 258 398 326 339 216 399 305 84 275 192 251 124 449 138 472 491 28 250 402 65 349 128 370 304 480 467 423 128 246 212 185 369 31 434 90 248 349 261 109 5 45 38 264 203 12 115 176 168 45 351 134 311 20 36 253 270 238 491 433 461 84 184 69 372 369 63 336 237 352 262 436 354 129 351 301 440 259 376 129 336 274 350 264 100 266 415 26 5 495 447 366 195 202 364 61 34 316 345 308 157 130 40 486 64 69 203 33 437 302 437 135 6 444 325 48 480 365 79 362 292 55 310 291 283 472 60 54 370 284 75 77 252 69 160 294 38 3 206 193 461 5 238 441 466 80 21 105 428 315 269 0 227 90 23 336 336 446 272 79 441 213 286 240 498 7 270 145 296 369 136 36 5 413 35 363 85 341 257 471 115 290 309 161 450 372 267 116 394 429 83 77 386 411 14 380 496 262 138 390 367 201 309 307 423 284 471 467 238 414 55 47 141 220 410 133 414 201 226 40 461 403 431 128 389 287 263 374 308 104 383 58 358 405 44 310 66 363 311 114 149 393 401 221 267 247 138 183 114 282 52 271 202 338 370 451 446 43 41 389 429 16 15 353 421 180 362 104 410 75 171 383 354 397 92 136 448 161 175 416 127 345 204 266 172 380 113 478 62 252 127 350 276 161 428 314 288 326 55 6 164 58 323 219 398 414 88 497 68 37 326 111 303 259 40 4 159 163 456 443 124 51 3 169 431 457 335 425 200 243 151 159 159 438 355 249 404 264 425 495 171 363 283 189 308 189 222 222 380 301 314 287 28 174 419 121 437 267 336 311 245 395 413 159 191 286 242 199 309 331 302 383 266 379 54 477 386 397 383 448 442 56 457 329 215 459 96 398 499 171 186 4 53 346 111 432 252 121 82 473 360 367 461 400 20 237 70 444 287 249 427 233 149 475 75 58 436 36 258 290 480 161 191 407 302 224 479 424 459 181 357 153 313 188 376 79 262 73 81 198 381 172 457 117 269 18 409 109 291 407 364 106 476 285 77 333 211 25 26 303 160 185 368 152 40 210 260 244 319 7 489 254 8 461 351 202 195 92 123 484 121 134 380 381 207 199 425 269 80 77 228 66 93 33 339 65 422 413 293 170 107 107 319 304 158 442 451 341 282 127 196 95 381 419 272 473 90 347 399 76 22 5 333 465 464 109 77 425 418 145 194 266 274 353 410 378 65 342 374 453 47 462 266 31 267 221 441 462 4 354 318 254 156 67 56 275 136 245 244 339 33 51 153 355 397 14 296 445 4 417 204 172 469 421 51 20 324 136 363 25 222 290 124 210 218 88 350 28 170 221 154 353 81 409 92 126 211 268 287 388 368 59 28 426 420 277 196 393 406 324 445 58 210 480 339 260 185 225 439 50 16 69 476 423 424 29 440 218 416 280 157 189 288 188 440 436 468 248 161 195 380 81 101 212 98 161 376 129 380 464 247 186 92 1 230 378 234 121 93 332 337 395 224 276 12 396 462 178 110 307 26 73 223 195 13 236 478 51 35 145 439 395 470 311 242 446 323 222 493 159 486 192 297 440 196 450 28 499 463 419 37 374 490 352 425 394 298 329 332 356 164 79 275 205 307 51 469 278 285 62 231 18 489 277 244 226 403 151 173 253 439 416 65 282 411 228 53 398 148 484 110 191 71 344 111 109 428 326 473 127 226 451 19 101 8 359 323 479 292 226 94 174 230 484 279 381 227 304 451 100 151 20 419 423 379 456 483 229 235 81 382 263 415 312 278 450 188 236 373 174 430 467 447 183 376 428 118 241 463 360 44 150 470 442 28 370 297 410 472 480 137 284 253 16 472 478 167 168 141 189 394 198 6 468 5 458 116 111 218 304 335 282 299 69 470 350 204 295 225 270 469 378 46 390 69 320 368 188 194 423 483 333 315 461 292 335 279 84 499 422 412 340 374 127 264 246 20 331 303 446 379 45 446 271 109 416 242 133 233 55 179 19 333 498 258 50 215 208 398 174 41 469 459 260 234 366 496 363 453 498 414 251 95 151 115 339 212 169 112 126 241 367 219 56 281 344 10 269 325 476 228 474 494 187
样例输出
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